Chapter 8. Examination of Tsunami Wave Force Evaluations, Sediment Transport
Calculations and Debris Impact Force
8.1. Tsunami wave force evaluation formula specifics
8.1.1. Evaluation formulae for tsunami wave force acting on maritime structures(1) Evaluation formula for tsunami wave force acting on upright maritime structures
Formulae, which have previously been proposed, are presented below for assessing tsunami
wave force acting on upright maritime structures.
1) Cases where soliton fission occurs
The impulsive tsunami wave force becomes larger when longwave tsunami head disperses
into multiple shortwaves (soliton fission) developing bores-shaped waves. The evaluation
formula presented by Ikeno et al. (2005) is the one that evaluates the corresponding tsunami
wave force (modified Tanimoto formula).
The Ministry of Land, Infrastructure, Transport and Tourism (2013) presented conditions
that take into account soliton fission based upon incident tsunami height and slope of sea
bottom. Yasuda et al. (2006) stated that a sufficient propagation distance is required for soliton
fission to develop. In addition to such knowledge, there are also methods that use analyticalmodels capable of calculating soliton fission (one-dimensional analysis, etc.) to verify thepresence of soliton fission.
[1]When water level at rear side of leading wave is higher than still water level*  3.0aI
p1  3.0 0 gaI
pM  p1
where, η*: tsunami wave pressure working height from the static water surface, aI: height(amplitude) of incident tsunami from static water surface, 0g: weight per unit volume ofseawater, p1: tsunami wave pressure intensity on static water surface, and pM: uplift pressure
at upstanding wall front-side lower edge.
[2]When water level at rear side of leading wave is lower than still water level *  3 .0 a I
p1  3.0  0 ga I
p 2   0 g B
pM  p1
p L  p2

Appendix 8 - 1

where, η*: tsunami wave pressure working height from the static water surface, aI: height(amplitude; numerical simulation results in the height of incident tsunami from static water
surface aI is ½ of the tsunami height) of incident tsunami from static water surface, 0g:
weight per unit volume of seawater, p1: tsunami wave pressure intensity on static water
surface, p2: negative pressure on outer surface of upstanding wall, pM: uplift pressure at
upstanding wall front-side lower edge, and pL: uplift pressure at upstanding wall backside
lower edge.

(Outside the harbor)(Inside the harbor)

Caissonp1

pM

Foundation mound[1]When water level at rear side of leading wave is higher than still water level(Inside the harbor)(Outside the harbor)

B
Caisson

pL
p1

pM

p2
Foundation mound[2]When water level at rear side of leading wave is lower than still water level
Figure 8.1.1-1 Schematic view of the evaluation formula presented by Ikeno et al. (2005)
2) Cases where soliton fission does not occur and does not overflow
If the water level fluctuates moderately, then it is possible to approximate hydrostaticpressure. However, even when soliton fission does not occur, tsunami wave force takes into
consideration effect of shoaling waves andwave breaking. In such a case, the evaluation
formula, which was presented by Tanimoto et al. (1984) (Tanimoto formula) and given in“Technical Standards and Accompanying Commentary for Port and Harbor Facilities” (Portsand Harbours Association of Japan, 2007), is applied to conditions where overflow does notoccur.

Appendix 8 - 2

[1]When water level at rear side of leading wave is higher than still water level*  3.0aI
p1  2.20 gaI
pM  p1
where, η*: tsunami wave pressure working height from the static water surface, aI: height(amplitude; numerical simulation results in the height of incident tsunami from static water
surface aI is ½ of the tsunami height) of incident tsunami from static water surface, 0g:
weight per unit volume of seawater, p1: tsunami wave pressure intensity on static water
surface, pM: uplift pressure at upstanding wall front-side lower edge, and pL: uplift pressure
at upstanding wall backside lower edge.
[2]When water level at rear side of leading wave is lower than still water level *  3 .0 a I
p1  2.2  0 ga I

p 2   0 g B

p M  p1

p L  p2

where, η*: tsunami wave pressure working height from the static water surface, aI: height(amplitude; numerical simulation results in the height of incident tsunami from static water
surface aI is ½ of the tsunami height) of incident tsunami from static water surface, 0g:
weight per unit volume of seawater, p1: tsunami wave pressure intensity on static water
surface, p2: negative pressure on outer surface of upstanding wall, pM: uplift pressure at
upstanding wall front-side lower edge, and pL: uplift pressure at upstanding wall backside
lower edge.

Appendix 8 - 3

(Outside the harbor)(Inside the harbor)

Caissonp1

pM

Foundation mound[1]When water level at rear side of leading wave is higher than still water level(Inside the harbor)(Outside the harbor)

B
Caisson

pL
p1

pM

p2
Foundation mound[2]When water level at rear side of leading wave is lower than still water level
Figure 8.1.1-2 Schematic view of the evaluation formula presented by Tanimoto et al. (1984)
3) Cases where soliton fission does not occur but overflow does
If soliton fission does not occur and overflow does occur, the evaluation formula, which
is presented in “Tsunami-Resistant Design Guideline for Breakwaters” (Ministry of Land,
Infrastructure, Transport and Tourism, 2013), is applied that has been corrected for thehydrostatic pressure difference (maximum water level difference) acting on the front and backsides of the target structure.
If an evaluation formula is applied that is based upon hydrostatic pressure difference in astate where there is slight overflow, it is possible that applying the Tanimoto formula in a state
where there is overflow immediately in front of where the water level is even lower may resultin significant tsunami wave force, so both are compared and the greater value adopted.

p1  a f  0 g  f  h
p2  f  hcp1
 f  hp3  ar  0 g  r  h
where, p1: tsunami wave pressure intensity on front-side bottom of upstanding wall, p2: tsunami
wave pressure intensity on front-side top of upstanding wall, p3: tsunami wave pressure
intensity on backside bottom of upstanding wall, 0g: weight per unit volume of seawater, h':water depth at bottom surface of upstanding wall, hc: height from static water surface to top of
upstanding wall, f: tsunami height from static water surface in front-side of upstanding wall,
af: hydrostatic pressure correction coefficient in front-side of upstanding wall based on
Appendix 8 - 4

hydraulic model experiment results (=1.05), and ar: hydrostatic pressure correction coefficientbehind upstanding wall based on hydraulic model experiment results (=0.9).

(Front side)(Rear side)

Water level at front of the breakwater

p2

f
hc

h

r
Caissonh
p1Foundation moundp3

Figure 8.1.1-3 Schematic view of the evaluation formula presented by Ministry of Land,
Infrastructure, Transport and Tourism (2013)(2) Formulae for assessing tsunami wave force acting on sloped maritime structures
Based upon Mizutani and Imamura (2000) and Mizutani and Imamura (2002), the tsunami
wave force acting on sloped maritime structures is classified as described below in accordancewith the conditions in which such force occurs.
• Hydro dynamic pressure and impulsive hydro dynamic pressure: These develop on the
moment when incident tsunami strikes a structure. Impulsive hydro dynamic pressure islargely related to the slope in front of the structure and there is a high probability of
impulsive hydro dynamic pressure developing when the slope is almost vertical if notcompletely.
• Run-up pressure: After the strike of an incident tsunami, run-up pressure develops when
the water level rises significantly as waves continue to arrive.
• Impact continuous pressure and impulsive impact continuous pressure: These develop
instantaneously as the result of the strike of reflective tsunami and incident tsunami. Whenthe dimensionless value Δp/ρgH is 2.0 or greater based on the wave height for thedifference with run-up pressure, this is referred to as impulsive impact continuous pressure.
• Overflow pressure and impulsive overflow pressure: These develop due to a tsunami that
overflows a sloped structure. If the flow velocity at crest and rear slope angle are high, theoverflow pressure increases and impulsivity increases.
For each of the aforementioned classifications, formulae, which have previously been
proposed, are given below for assessing tsunami wave force acting on sloped maritime structures.
1) Hydro dynamic pressure and impulsive hydro dynamic pressure (Fukui et al., 1962; Mizutani
and Imamura, 2000; Mizutani and Imamura, 2002)

Appendix 8 - 5zpd z   pdm 1  1.4 
R


z

  0 ; Above the static water surface
R
(Fukui et al., 1962)z
p d  z   p dm 1  
R



3

z

  0 ; Above the static water surfaceR(Mizutani and Imamura, 2000)z pd  z   pdm 1 
 2R z  0 ; Below the static water surface
R(both of the above references)where, pd: hydro dynamic pressure distribution, R: run-up height, and z: positive coordinates
upward from the static water surface. Also, pdm is the hydro dynamic pressure or impulsivehydro dynamic pressure, and it is calculated using wave velocity c according to the following
equation.

pdm  0.12

wc 4
; Hydro dynamic pressure (Mizutani and Imamura, 2000)
g 2H

pdm  0.25

wc 4
; Impulsive hydro dynamic pressure (Mizutani and Imamura, 2002)
g 2H

c

g H  h H  2 h 
2 H  h    H 

where, w: weight per unit volume of water, h: water depth, η: resistance coefficient (Fukui etal., 1962) and H: incident wave height. Also, the conditions for development of impulsivehydro dynamic pressure are shown in the following equation using dip-slope angle θ1 in the
structure front-side.

c2
 0.6 cot 1  3.45
gH2) Run-up pressure (Mizutani and Imamura, 2000)

psm  0.142  cos1   pdm
psm  0.38 pdm

c2
gH

c2
gH

(0 < cosθ1 0.71)(0.71 < cosθ1)

where, psm: maximum sustained tsunami wave pressure, pdm: hydro dynamic pressure, θ1: dipslope angle in the structure front-side, c: bore wave velocity, and H: incident wave height. Also,
sustained tsunami wave pressure distribution ps is expressed with the following equation.

z
ps  z   psm 1  2.5 
R


z

  0 ; Above the static water surface
R
Appendix 8 - 6z ps  z   psm 1   3R z  0 ; Below the static water surface
R

where, R: run-up height and z: positive coordinates upward from the static water surface.
3) Impact continuous pressure (Mizutani and Imamura, 2000)• Case where the dip-slope angle θ1 in front of the structure is comparatively steep

pim  0.5 p dm  p sm (hcotθ1≤0.15m)

where, pim: maximum impact continuous pressure, psm: maximum sustained tsunami wave
pressure, pdm: hydro dynamic pressure, and h: water depth. Also, the impact tsunami wave
pressure distribution pi is expressed with the following equation.

zpi z   pim  0.9  3 
R


z

  0 ; Above the static water surfaceR

pi z   0.9 pimz  0 ; Below the static water surface
R

where, R: run-up height and z: positive coordinates upward from the static water surface.
• Case where the dip-slope angle θ1 in front of the structure is 45 degrees or less and thestatic water depth is deeppim  0.5 pdm  p sm   2200

(0.15m>hcotθ1)

where, pim: maximum impact continuous pressure, psm: maximum sustained tsunami wave
pressure, pdm: hydro dynamic pressure, and h: water depth. Also, the impact continuouspressure distribution pi is expressed with the following equation.

zpi z  pim  2 10 
R


z

  0.1 ; Above the static water surface

R

z

pi  z   pim  0.35  6.5 
R


z


 0   0.1 ; On the static water surfaceRpi  z   0.35 pimz  0 ; Below the static water surface
R

where, R: run-up height and z: positive coordinates upward from the static water surface.
4) Overflow pressure and impulsive overflow pressure (Mizutani and Imamura, 2002)

p om
V sin  2
2 2 m
gH d 2gH d 2pom
V sin  2 
 2 2 m
gH d 2 gH d 2 ; Overflow pressure
4; Impulsive overflow pressure

where, pom: maximum overflow pressure, Hd2: rear surface height, Vm: maximum flow
velocity at crest, and θ2: rear surface slope angle. Also, the maximum overflow pressure pom
is expressed with the following equation.
Appendix 8 - 7

pom  AVm 2 gH d 2 sin  2
where, A: coefficient determined empirically, and ρ: water density. Also, the conditions fordevelopment of impulsive overflow pressure are given with the following equation.

2 2

Vm sin  2
gH d 2

1

8.1.2. Evaluation formula for tsunami wave force acting on land structures
The formulae for assessing tsunami wave force acting on land structures may be classified into
evaluation formulae using hydraulic quantity not affected by the structure, which is obtained by meansof a tsunami run-up calculation without the structure subject to evaluation, and evaluation formulaeusing hydraulic quantity affected by the structure which is obtained by means of a tsunami run-up
calculation that takes into account the target structure. The previously proposed formulae for assessing
tsunami wave force acting on land structures are shown below according to this classification.
(1) Evaluation formulae based on hydraulic quantity in a state without a structure1) Evaluation formula using maximum inundation depth
For the evaluation formula based on hydraulic quantity in a state without a target structure,and evaluation formula that regards tsunami wave pressure as a hydrostatic pressure equivalent
to three times the maximum inundation depth of a progressive wave (Asakura et al., 2000) has
generally been used widely, and also referenced in the guidelines for tsunami evacuationbuildings (Cabinet Office, 2005).

pmax  z   g hi max  z 

where, z is the height from the ground surface, ρ is the fluid density, g is the gravitational
acceleration, and himax is the maximum inundation depth of a progressive wave in a state
without structures. is the water depth coefficient, and = 3.0 when the Froude number,which is calculated using the maximum inundation depth and maximum flow velocity, is 1.5
or greater, and = 1.0 when the Froude number is close to 1.0 (hydrostatic pressure), but =
3.0 has been proposed as a value capable of enveloping all data.
The National Institute for Land and Infrastructure Management (2012) proposed a
reduction in the Asakura et al. (2000) water depth coefficient dependent upon the distance fromthe coastline and the presence of shielding, which was based on the results of a consolidation
using the Froude number for field data.
On the other hand, Sakakiyama (2012) and Ishida et al. (2014) confirmed based upon
hydraulic model experiment and analysis, when the Froude number exceeds 1.5, the water
Appendix 8 - 8

depth coefficient exceeds 3, and it is desirable to appropriately set the water depth coefficient in keeping with the Froude number.
Also, Ikeno et al. (2006) proposed the following formula because the results of hydraulicmodel experiment simulating soliton fission waves showed that, when the run-up water depth
is lower, the overflow water mass surges higher when the wave strikes a land structure and thewater depth coefficient  is relatively great.
• Main tsunami wave pressure P1

P1 z /(gmax)  z /max • Soliton fission wave predominant portion tsunami wave pressure P2

P2 z /(gmax)  K1(Z /(K2max) )• Acting tsunami wave pressure P
P  z   max P1  z , P2  z 

 1.35/(max / h) 1.5 ；0.3 max / h  0.9
K1  1.8, K2  1.35/ 
where, z: height from the ground surface, ρ: fluid density, g: gravitational acceleration, ηmax:
maximum amplitude of level of progressive wave at structure location, : water depth
coefficient, and h: water depth in front of revetment, and the tsunami wave pressure of themain tsunami wave is calculated using P1, and the difference between P1 and P2 is added if
there is action of the soliton fission wave.
Cabinet Office (2005) stated that of the tsunami wave pressures in a triangular distribution
based upon Asakura et al. (2000) when tsunami overflows a structure, the trapezoidal
distribution acts up to the height where a structure is present. By contrast, the Fire and Disaster
Management Agency (2009) proposed, based upon hydraulic model experiments and an
examination using CADMAS-SURF, a formula that reduces the tsunami wave pressure acting
on the bottom surface in accordance with the ratio of inundation depth to oil weir height.

Pmax  1   d g max
 0.692hc  max 2  2.352hc  max d  

 2. 0hc  max  1.7 
hc  max  1.7 

where, hc: oil weir height, ηmax: maximum inundation depth of progressive wave, and ad:
dynamic pressure coefficient.
2) Evaluation formula using maximum inundation depth and flow velocity• Hydrostatic pressure-type evaluation formula
Asakura et al. (2002) consolidated empirical data on cross-sectional two-dimensional
structures and three-dimensional structures, and took into account the effect of flow velocity
by regarding the factor α in Asakura et al. (2000) as a function of the Froude number.
Appendix 8 - 9  1.2 Fr  1.0
where, Froude number Fr is calculated according to the following formula using the
maximum inundation depth ηmax and flow velocity uη at the time such inundation occurs.

Fr  ug max

Sakakiyama (2012) arranged the factor α in Asakura et al. (2000) as a function of the
Froude number based upon numerical simulations of cross-sectional two-dimensional
structures. The Froude number Fr is defined the same as in Asakura et al. (2002).

  1.4Fr  1.0• Drag-type evaluation formula
Omori et al. (2000) evaluated tsunami wave force in the time series based upon themodified Morison equation.

1
1d
FH  CDu u B  CM uBL  CS  u u B  gBL22dx
where, CD: drag coefficient (=2.05), CM: inertial force coefficient (=2.19), CS: impact force
coefficient (=3.6tanθ, θ: wave surface angle), u: horizontal flow velocity of tsunami
progressive wave, u : horizontal acceleration of tsunami progressive wave, : inundation
depth due to tsunami progressive wave, B: structure width, and L: structure length. The righthand side first term is the term for drag, right-hand side second term is the term for inertial
force, right-hand side third term is the term for impact force, and right-hand side fourth termis the term for the hydraulic gradient force.
• Evaluation formula for tanks
The Fire and Disaster Management Agency (2009) proposed a method for outdoor
storage tanks which calculates the tsunami wave force using maximum inundation depth
and maximum flow velocity in a state where an oil weir is present but there are no tanks.
Horizontal tsunami wave force FdH
FdH 





2
1 
g hxmax   R cosd



2
3

hxmax     max  p m cos mm 0

p 0  0.680,

p1  0.340,

p 2  0.015,

p3  0.035

where, α: inundation depth coefficient related to horizontal tsunami wave force (1.8
according to previous reviews) uses the value in the following formula according to the
Froude number found based on maximum inundation depth and maximum flow velocity ina state where no tanks have been set up.

Appendix 8 - 10

Fr  1.3 1.8
  2.0Fr  0.8
 1.0


1.3  Fr  0.9
0.9  Fr 

Vertical tsunami wave force FtV

FtV  2 ghVmax  R 2 cos 2 d03hVmax     max  q m cos mm 0q0  0.720,

q1  0.308,

q 2  0.014,

q3  0.042

where, : inundation depth coefficient related to vertical tsunami wave force uses the value
in the following formula according to the Froude number found based on maximum
inundation depth and maximum flow velocity in a state where no tanks have been set up.
 1.2  0.5Fr  0.55
 1.0
Fr  1.3

1.3  Fr  0.9
0.9  Fr (2) Evaluation formulae based on hydraulic quantity in a state with a structure1) Evaluation formula using inundation depth in front of structure
Iizuka and Matsutomi (2000) proposed an evaluation formula that uses inundation depth
in front of structure.

1
1
FD  CDu 2 A  CDu 2 h f B  0.61 wCD h2f B22
where, CD: drag coefficient,u: flow velocity on land, A: structure inundation area, hf:
inundation depth in front of the structure, B: structure width, and w: weight per unit volumeof fluid.
2) Evaluation formula using inundation depth and flow velocity in front of structure
Arimitsu et al. (2012) proposed the following formula for finding the time series of thetsunami wave pressure vertical distribution by using inundation depth and flow velocity infront of the structure.

p z, t   gh f t   z u f t 

2where, ρ: fluid density, g: gravitational acceleration, z: action location, and t: time.
The aforementioned formula is the distribution of hydrostatic pressure according toinundation depth hf in front of the structure when a structure is present and the pressure, whichis in keeping with the horizontal flow velocity uf based upon the law of conservation of
momentum, is acting upon the structure.

Appendix 8 - 11

3) Evaluation formula using inundation depth and flow velocity in the offing at a distance of fivetimes the tsunami depth from the structure
Kihara et al. (2012) and Takabatake et al. (2013) focused on structures having a width
equivalent to between 0.5 to 5 times the depth of inflow, and proposed the following formulawhich uses inundation depth and flow velocity in the offing at a distance of five times the depthof the inflowing tsunami from the structure.
2

u2 


1 
u2
F  g hin  in  W , p   g  hin  in  z 
2 
2g 
2g



where, hin and uin: inundation depth and flow velocity at a point that is five times a
representative inflowing tsunami depth in an upstream direction from the target structure, and
W: structure width.
(3) Hydraulic quantity used in calculation of tsunami wave force
Sections (1) and (2) present formulae for assessing tsunami wave force acting on land
structures that are separated into cases where hydraulic quantity is used in a state where there are
no structures and hydraulic quantity in a state where there are structures present. In addition, thehydraulic quantities used may be classified into cases where only inundation depth is used andcases where both inundation depth and flow velocity are used.
The maximum inundation depth used in evaluation formulae presented by Asakura et al.
(2000), Cabinet Office (2005), and the Ministry of Land, Infrastructure, Transport and Tourism(2012) is the maximum inundation depth of a progressive wave that does not include the effectof reflection from land. Also, the evaluation formula presented by Iizuka and Matsutomi (2000)
uses the inundation depth in front of the structure.
The evaluation formulae presented by Asakura et al. (2002) and Sakakiyama (2012) used
the maximum inundation depth of a progressive wave as well as the Froude number found fromthe maximum inundation depth and the flow velocity at the time the maximum inundation depth
occurs. The Fire and Disaster Management Agency (2009) also used the maximum inundation
depth and the Froude number. However, for calculating the Froude number, the Fire and Disaster
Management Agency (2009) used the maximum inundation depth and maximum flow velocity
when the occurrence times are different.
The evaluation formulae presented by Omori et al. (2000), Arimitsu et al. (2012), Kihara etal. (2012), and Takabatake et al. (2013) used the time series of inundation depth and flow velocity.
(4) Classification of tsunami wave pressure
Arikawa et al. (2005) classified the tsunami wave pressure acting on an upstanding wall
according to the time series (see Main Volume Section 6.5.2). The evaluation formulae presented
Appendix 8 - 12

by Omori et al. (2000) and Arimitsu et al. (2012) take into account impulsive hydro dynamic
pressure positively, and it is possible to calculate both hydro dynamic pressure and continuouspressure. On the other hand, the evaluation formulae presented by Iizuka and Matsutomi (2000),
Kihara et al. (2012), and Takabatake et al. (2013) focused only continuous pressure. The
evaluation formulae presented by Asakura et al. (2000), Cabinet Office (2005), Ministry of Land,
Infrastructure, Transport and Tourism (2012), Fire and Disaster Management Agency (2009),
Asakura et al. (2002), and Sakakiyama (2012) arrange maximum tsunami wave force and tsunami
wave pressure without regard to causal factors, and the proposed equations comprised both
impulsive hydro dynamic pressure and maximum continuous pressure.
(5) Shape of target structure
Structure shapes may be classified into three-dimensional structures such as buildings inwhich a tsunami flows into the structure to the back through sides of the structure, and twodimensional structures such as seawalls that are uniform in a cross direction and the tsunami does
not flow through to the back with the exception of overflow.
The evaluation formulae presented by Asakura et al. (2000), Sakakiyama (2012), andTakabatake et al. (2013) focused on two-dimensional structures where the tsunami does not wrap
around the sides. The Fire and Disaster Management Agency (2009) formula for assessing
tsunami wave force acting on oil weirs has also been reviewed using vertical two-dimensional
calculations. The focus of the evaluation formulae presented by the Cabinet Office (2005) andthe Ministry of Land, Infrastructure, Transport and Tourism (2012) are three-dimensional
structures. The evaluation formulae presented by Omori et al. (2000) and Iizuka and Matsutomi(2000) focused on three-dimensional structures, and the focus of the Fire and Disaster
Management Agency (2009) formula for assessing tsunami wave force acting outdoor storage
tanks was a three-dimensional structure. Kihara et al. (2012) focused on three-dimensional
structures having a width equivalent to between 0.5 and 5 times the inflow depth. Asakura et al.
(2002) and Arimitsu et al. (2012) focused on both two-dimensional structures and threedimensional structures.
8.1.3. Examples of tsunami wave force acting on the ground in the vicinity of structures, etc.
8.1.3.1. Simplified calculation method for pressure acting on ground surface as presented by Omura
et al. (2014)
Omura et al. (2014) used a simplified calculation to find the pressure acting on the ground surface
behind a seawall when a tsunami overflows the seawall and falls to the ground surface.
Appendix 8 - 13

The simplified calculation regards the horizontal flow velocity vx of the portion overflowing theseawall as (gh)0.5 (h is the overflow depth, and g is the gravitational acceleration), and the overflow
motion is assumed to be a parabolic drop motion to find the flow velocity v, strike angle θ, andovertopping wave distance s, and using these as conditions, calculates the maximum hydro dynamic
pressure pd without a water cushion following the evaluation of dynamic pressure of the freefall-type
energy dissipater for a dam (Japan Society of Civil Engineers, 1971).
pd (v sin  ) 2g2g
s  vxt，v  v x2  v z2

，  tan 1 (v z v x )v x  gh，v z  gt，t 

2 ( H  0. 5h )gwhere, ρ: water density, vx: horizontal flow velocity, vz: vertical flow velocity, t: time, and H: heightof seawall.
8.1.3.2. Simplified estimation method for overflow routes, etc. as presented by Mitsui et al. (2015)(1) Simplified estimation method for overflow routes
Mitsui et al. (2015) presented the following simplified method for estimating overflow
routes of tsunami overflowing a breakwater.
• Caisson dimensions and tsunami height are already known. (Figure 8.1.3.2-1).
• The calculation diagram presented by Mitsui et al. (2015) is used to read flow rate coefficientm, h2/h1, and u2z/u2x.
• Water route thickness h2 at the caisson heel is found based on the read h2/h1, and flow
velocities u2x and u2z may be calculated using the following formula.
u2 x  q h2 ， q  mh1 2gh1

• The trajectory of the overflow route assumed that water particles fall freely from the caisson
heel, and flow velocities u3x and u3z as well as water landing location x3 are determined asshown below.
u 3 x  u 2 x，u3 z   u 22 z  2 g (d1  h2 2)，x3  u2 x

u2 z  u 22 z  2 g (d1  h2 2)g• The route thickness h3 at the water landing location is determined using the following
formula, and the trajectory under the water surface inside the port is assumed to be a straightline.
h3  qu32x  u32z

Appendix 8 - 14

Mitsui et al. (2015) used the aforementioned simplified estimation method to calculate theroute trajectory, and stated that, for the most part, the empirical results, numerical analysis results,
and results using the simplified estimation method coincide.

Wave-dissipating
blocksCaisson

Mound(Left side: Sectional view of breakwater, Right side: Trajectory of the overflow nappe)
Figure 8.1.3-1 Size definition of an estimation method for the trajectory of the overflow nappe
proposed by Mitsui et al. (2015)(2) Method for estimating driving flow velocity
Mitsui et al. (2015) also presented a method for estimating the driving flow velocity towards
mounds inside a port. The results presented by Mitsui et al. (2015) stated that good estimation
results were able to be obtained for the most part when C1=3.0. The method for estimating driving
flow velocity is described below.
• Based upon flow velocity U0 for the overflow route on the water surface inside the port, theflow velocity driving toward mounds inside the port is estimated.
• Rajaratnam (1976) presented the following formula based on a theoretical solution andprevious empirical results for flow velocity at the central axis of a two-dimensional water
jet spouting from a nozzle.
um U 0  C1

x b0 ，

C1  3.5

where, U0 is the flow velocity at the exhaust nozzle, um the flow velocity on the central axis,
b0: 1/2 of the exhaust nozzle width, x : the distance from exhaust nozzle, and C1: theempirical constant.
• When this is applied to the overflow route and considered, U0 is the absolute value of theflow velocity at the location of the water surface inside the port, 2b0 is the route thickness
on the water surface, x is the distance from the water landing location to the mounddriving location, and the flow velocity um driving towards the mound is determined based
upon the relationship in the aforementioned formula.

Appendix 8 - 15

8.1.4. Verification of the validity of tsunami wave force evaluation formulae
8.1.4.1. Examination overview
The results of experiments performed by Kihara et al. (2015) on tsunami and flood flow channels
were used to examine the applicability of formulae for assessing tsunami wave force acting on land
structures. This examination focused on tsunami wave force acting on seawall (two-dimensional
structures) and cuboids (three-dimensional structures). Also, an examination of tsunami wave force
was conducted utilizing the results of numerical simulations based upon a plane two-dimensionalmodel.
8.1.4.2. Tsunami wave force acting on seawall (two-dimensional structures)(1) Experiment overview
Figure 8.1.4-1 shows the experimental device for the test to assess tsunami wave force acting
on a seawall (two-dimensional structure). The water channel is 2.5 m high and 4 m wide. A
tsunami is created within the water channel by cooperation of a flow rate control valve and jet
flow control gate, which are installed upstream in the water channel, and a movable weircontrolling sub-critical flow, which is installed downstream.
[Plan view]
Water channel side wall

Seawall

Upstream
Downstream end

Water channel side wall

[Sectional
view]
【断面図】
Upstream

Downstream

Water channel bed

H1, H2, H3, H4: Measuring points of inundation depth, V1, V3: Measuring points of horizontal flow velocity by ADV,
V2: Measuring point of horizontal flow velocity by Aquadopp profiler, PV1 - PV25: Measuring points of wave pressure

Figure 8.1.4-1 Experimental device for the test to assess tsunami wave force acting on a tide seawall(two-dimensional structure)

Appendix 8 - 16

For the experiment, a model of a seawall was set up, which was 1.5 m high and 4.0 m wide,
near the center of the water channel, and measurements of the inundation depth, flow velocity,and pressure were taken for seven (Cases 1 through 7) tsunami shapes having different inundation
depths and flow velocities upstream of the seawall. Figure 8.1.4-2 shows the inundation depths
upstream of the seawall, flow velocity, and Froude number time series tsunami shapes.

H1: Inundation depth

H2: Inundation depth
case1
case4
case7

2.5

case2
case5

3.0

case3
case6

Inundation depth (m)Inundation depth (m)

3.0

2.0
1.5
1.0
0.5
0.0

5.0

case3
case6

4.0
3.0
2.0
1.0
0.0

Vertical flow velocity (m/s)

Vertical flow velocity (m/s)

6.0

2.0
1.5
1.0
0.5

5.0

case2
case5

case3
case6

3.0
2.0
1.0
0.0

H2·V2: Froude number
case1
case4
case7

5.0

case2
case5

case3
case6

4.0
Fr

4.0
Fr

case3
case6

4.0

6.0
case1
case4
case7

case2
case5

‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Time (sec)

H1·V1: Froude number

5.0

case1
case4
case7

6.0

‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Time (sec)

6.0

V2: Flow velocity

7.0
case2
case5

case3
case6

‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Time (sec)

V1: Flow velocity
case1
case4
case7

case2
case5

0.0

‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Time (sec)

7.0

case1
case4
case7

2.5

3.0

3.0

2.0

2.0

1.0

1.0

0.0

0.0
‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Time (sec)‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Time (sec)Figure 8.1.4-2 Time series of inundation depth upstream of the seawall, flow velocity, and Froudenumber(2) Tsunami wave force calculation methods
Tsunami wave force evaluation formulae used for comparison with empirical results are
given below. The most appropriate positional data was selected from among the geodetic points
Appendix 8 - 17

for the empirical inundation depths and flow velocities used in the calculation of tsunami wave
force.
1) Tsunami wave force evaluation formula using hydraulic quantity in a state without structures• Tsunami wave force evaluation formula presented by Asakura et al. (2000) (water depth
coefficient α=3.0)
Since the maximum inundation depth of the progressive wave was not measured in theexperiment, the maximum inundation depth at point H2 where the structure exists was used
0.5 times for the stability of the tsunami wave force assuming the condition of perfect reflection.
2) Tsunami wave force evaluation formula using hydraulic quantity in a state with structures• Tsunami wave force evaluation formula presented by Arimitsu et al. (2012)
To calculate the tsunami wave force, the empirical results were used for inundation depth
and flow velocity at points H2 and V2.
• Tsunami wave force evaluation formula presented by Takabatake et al. (2013)
To calculate the tsunami wave force, the empirical results were used for inundation depth
and flow velocity at points H1 and V1.
(3) Results of tsunami wave force calculations
1) Tsunami wave force evaluation formula using hydraulic quantity in a state without structures
Figure 8.1.4-3 is a comparison of the maximum tsunami wave pressures as measured bytsunami wave pressure meters in experiments and the maximum tsunami wave pressure
according to the evaluation formula presented by Asakura et al. (2000). In all of the cases as
well, the maximum tsunami wave pressure according to the evaluation formula presented by
Asakura et al. (2000) was approximately 1.5 times the empirical results, obtaining results thatsufficiently encompass the empirical results.
2) Tsunami wave force evaluation formula using hydraulic quantity in a state with structures
Figure 8.1.4-4 shows the empirical results of a tsunami wave force time series acting ona seawall and the results of calculations using tsunami wave force evaluation formulae. The
features are shown below of each tsunami wave force evaluation formula, which have beenobtained from the results of comparisons of these formulae.
• In a quasi-steady state (t≥10s), the tsunami wave force resulting from the evaluation
formulae presented by Arimitsu et al. (2012) and Takabatake et al. (2013) coincided
approximately with the empirical results.
• In a non-steady state where dynamic pressure was intensely observed (t<10s), the tsunami
wave force resulting from the evaluation formula presented by Arimitsu et al. (2012)
generally coincided with the empirical results.
• The calculation formula presented by Takabatake et al. (2013) was applicable during a quasiAppendix 8 - 18

steady-state, and in a non-steady state where dynamic pressure was intensely observed(t<10s), a tsunami wave force was obtained, depending on the case, that significantly
surpassed the empirical results.
2.0

2.0

Case1

Asakura et al.(2000)
Experiment

1.0
0.5

2.0

2.0

4.0
p/ρg (m)

6.0

8.0

0.0
2.0

Case3

Asakura et al.(2000)

1.5

2.0

Case4

1.0
0.5

4.0
p/ρg (m)6.0

8.0

Asakura et al.(2000)

1.5

Experiment

z (m)

z (m)

Experiment

1.0

0.0
0.0

Experiment

1.0
0.5

0.0

0.0
0.0

2.0

2.0

4.0
p/ρg (m)

6.0

8.0

0.0
2.0

Case5

Asakura et al.(2000)

1.5

2.0

Case6

1.0
0.5

4.0
p/ρg (m)6.0

8.0

Asakura et al.(2000)

1.5

Experiment

z (m)

z (m)

Asakura et al.(2000)

0.5

0.0

Experiment

1.0
0.5

0.0

0.0
0.0

2.0

2.0

Case7

4.0
p/ρg (m)

6.0

8.0

0.0

2.0

4.0
p/ρg (m)6.0

Asakura et al.(2000)

1.5

z (m)

Case2

1.5

z (m)

z (m)

1.5

Experiment

1.0
0.5
0.0
0.0

2.0

4.0
p/ρg (m)6.0

8.0

Figure 8.1.4-3 Comparison of maximum Tsunami wave pressure acting on the seawall

Appendix 8 - 19

8.0

Experiment
50,000
case1
case3
case5
case7

F(N/m)

40,000

case2
case4
case6

30,00020,00010,0000‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Evaluation formula
Arimitsu et al. (2012)

presented

by

case1
case4
case7

case3
case6

Time (sec)

50,000
case2
case5

30,00020,000by

50,000
case1
case3
case5
case7

40,000F(N/m)

F(N/m)

40,000Evaluation
formulapresented
Takabatake et al. (2013)

case2
case4
case6

30,00020,00010,00010,0000

0‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Time (sec)‐5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

Time (sec)Figure 8.1.4-4 Empirical results of tsunami wave force time series acting on the seawall and results ofcalculations using tsunami wave force evaluation formulae
8.1.4.3. Tsunami wave force acting on cuboids (three-dimensional structures)(1) Experiment overview
Figure 8.1.4-5 shows the experimental device for the test to assess tsunami wave force acting
on cuboids (three-dimensional structures). For the experiment, a cuboid model was set up, which
had a height of 2.0 m and width of 1.0m×1.0m, near the center of the water channel. The
inclination of the cuboid model was varied, and measurements of the inundation depth, flow
velocity, and pressure were taken during three types of flows having different inundation depths
and flow velocities upstream of a seawall. Also, the inundation depth and flow velocity were
measured for a case where a cuboid model was not set up (progressive wave).
Figures 8.1.4-6 to 8.1.4-9 show the empirical results of the time series tsunami shape forinundation depth, flow velocity, and other properties. Of the flow velocities measured at locations
V1 and V2, consideration needs to be given to flow velocity during the periods of time indicatedbelow, because a vertical mean flow velocity did not form for between 5 to 10 seconds after areflected wave from the cuboid model and the movable weir at the downstream edge reached themeasurement point.

Appendix 8 - 20

Time periods when there is no vertical mean flow velocity·Case where cuboid model is not set up·Case where cuboid model set up

Type 1: t = 18s ~ 24s

Type 1: t = 11s ~ 16s

Type 2: t = 20s ~ 25s

Type 2: t = 15s ~ 20s

Type 3: t = 23s ~ 30s

Type 3: t = 10s ~ 20s【Plan view】

Upstream

TsunamiDownstream

Cuboid【Cuboid】
0 degreeSuper-critical flow control gate

Sub-critical flow control canal gate

【Sectional view】

TsunamiCuboid15 degree

TsunamiTsunami45 degree

Unit: mTsunami

H1 - H8: Measuring points of inundation depth
V1: Measuring points of horizontal flow velocity by ADV
V2, V3, V4: Measuring point of horizontal flow velocity by aquadopp profiler
Pressure: Measurement is performed by installing pressure sensors of 6 points, 18points, 6 points respectively on the verticalline of the left end, the center, and the right end of the side face of the pressure gauge.

Figure 8.1.4-5 Experimental device for the test to assess tsunami wave force acting on cuboids (threedimensional structures)

Appendix 8 - 21

type1
type2
type3

0

50

100

150
200
Time (sec)

250

300

V1: Flow velocity

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

Flow velocity (m/s)

Inundation depth (m)H2: Inundation depth
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

type1
type2
type3

0

350

50

150
200
Time (sec)

250

300

350

H2·V1: Froude number

H4: Inundation depth
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

5.0
type1
type2
type3

4.0

Fr

Inundation depth (m)

100

3.0
2.0

type1

1.0

type2
type3

0.0

0

50

100

150
200
Time (sec)

250

300

0

350

50

100

150
200
Time (sec)

250

300

Figure 8.1.4-6 Time series of inundation depth in case without the cuboid model, flow velocity, Froude

H2: Inundation depth

2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

θ=0 degree
θ=15 degree
θ=45 degree0

Flow velocity (m/s)

Inundation depth (m)number (Flow type: type1~type3)

V1: Flow velocity

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

θ=0 degree
θ=15 degree
θ=45 degree

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)

V2: Flow velocity
θ=0 degree
θ=15 degree
θ=45 degree0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)

Flow velocity (m/s)

Inundation depth (m)H3: Inundation depth
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

θ=0 degree
θ=15 degree
θ=45 degree0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)Figure 8.1.4-7 Time series of inundation depth and flow velocity in case with cuboid (Flow type:type1)

Appendix 8 - 22350

V1: Flow velocity
θ=0 degree
θ=15 degree
θ=45 degree0

Flow velocity (m/s)

Inundation depth (m)H2: Inundation depth
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)θ=0 degree
θ=15 degree
θ=45 degree

0

V2: Flow velocity
θ=0 degree
θ=15 degree
θ=45 degree0

Flow velocity (m/s)

Inundation depth (m)H3: Inundation depth
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)θ=0 degree
θ=15 degree
θ=45 degree0

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Time (sec)Figure 8.1.4-8 Time series of inundation depth and flow velocity in case with the cuboid model (Flowtype: type2)

V1: Flow velocity

θ=0 degree
θ=15 degree

Flow velocity (m/s)

Inundation depth (m)H2: Inundation depth
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

θ=45 degree

0

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340
Time (sec)θ=0 degree
θ=15 degree
θ=45 degree

0

V2: Flow velocity

θ=0 degree
θ=15degree

Flow velocity (m/s)

Inundation depth (m)H3: Inundation depth
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

θ=45 degree020 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340
Time (sec)

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340
Time (sec)

5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

θ=0 degree
θ=15 degree
θ=45 degree020 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340
Time (sec)Figure 8.1.4-9 Time series of inundation depth and flow velocity in case with the cuboid model (Flowtype: type3)

Appendix 8 - 23

(2) Tsunami wave force calculation methods
Tsunami wave force evaluation formulae used in comparisons with empirical results are
given below. The most appropriate positional data was selected from among the geodetic points
for the empirical inundation depths and current velocities used in the calculation of tsunami wave
force.
1) Tsunami wave force evaluation formula using hydraulic quantity in a state without structures• Tsunami wave force evaluation formula presented by Asakura et al. (2000) (water depth
coefficient α=3.0)
The experiment measured the maximum inundation depth of the progressive wave, andthe maximum inundation depth himax (type 1:1.18m, type 2: 1.62m, type 3: 1.65m) of the
progressive wave at point H4 was used to calculate the tsunami wave force.
• Tsunami wave force evaluation formula presented by Asakura et al. (2002)
To calculate the tsunami wave force, the maximum inundation depth himax and flow
velocity (time when himax occurs) of the progressive wave at points H2 and V1, which are
shown in Table 8.1.4-1, were used.
• Tsunami wave force evaluation formula presented by Sakakiyama (2012)
To calculate the tsunami wave force, the maximum inundation depth himax and flow
velocity (time when himax occurs) of the progressive wave at points H2 and V1, which are
shown in Table 8.1.4-1, were used.
Table 8.1.4-1 Hydroulic quantity and water depth coefficient of progressive wave at point H2 and V1
Flow

himax

uh

type

(m)

(m/s)

type1

1.28

0.56

type2

1.60

type3

1.68

α

α

(Asakura et al., 2002)(Sakakiyama, 2012)

0.16

1.19

1.22

0.26

0.07

1.08

1.09

0.18

0.04

1.05

1.06

Fr

2) Tsunami wave force evaluation formula using hydraulic quantity in a state with structures• Tsunami wave force evaluation formula presented by Arimitsu et al. (2012)
To calculate the tsunami wave force, the time series tsunami shapes of inundation depth
and flow velocity at points H3 and V2 were used.
• Tsunami wave force evaluation formula presented by Kihara et al. (2012)
To calculate the tsunami wave force, the time series tsunami shapes of inundation depth
and flow velocity at points H2 and V1 were used.
The flow velocity in the empirical results was the flow velocity in a horizontal direction
Appendix 8 - 24

(direction x as shown in Figure 8.1.4-5), so the flow velocity was corrected in accordance with
the inclination of the cuboid and used in the tsunami wave force evaluation formulae presented
by Arimitsu et al. (2012) and Kihara et al. (2012).
(3) Tsunami wave force calculation results
1) Tsunami wave force evaluation formula using hydraulic quantity in a state without structures
Figure 8.1.4-10 shows the results of a comparison of the maximum tsunami wave
pressures as measured by tsunami wave pressure meters in experiments and the maximum
tsunami wave pressure according to the evaluation formulae. The maximum wave pressure in
the empirical results is based on a zero degree inclination of the cuboid and measurement
aspect [1] where the maximum tsunami wave force is obtained.
The features are shown below for each tsunami wave force evaluation formula, whichhave been obtained from the results of comparisons of these formulae.
• The maximum tsunami wave pressure according to the evaluation formula presented by
Asakura et al. (2000) was approximately 3 times the empirical results, obtaining results thatsufficiently encompass the empirical results.
• The maximum tsunami wave pressure resulting from the evaluation formulae presented by
Asakura et al. (2002) and Sakakiyama (2012) generally coincide with the empirical results.
type1

2.5

Asakura et al. (2000)
Asakura et al. (2002)
Sakakiyama (2012)
Experiment

z (m)

2.0
1.5
1.0
0.5
0.0
0.0

type2

1.5

6.0

2.5

Asakura et al. (2000)
Asakura et al. (2002)
Sakakiyama (2012)
Experiment

2.0

z (m)

4.0
p/ρg (m)

8.0

type3

Asakura et al. (2000)
Asakura et al. (2002)
Sakakiyama (2012)
Experiment

2.0

z (m)

2.5

2.0

1.0
0.5

1.5
1.0
0.5

0.0

0.0
0.0

2.0

4.0
p/ρg (m)

6.0

8.0

0.0

2.0

4.0
p/ρg (m)6.0

8.0

Figure 8.1.4-10 Comparison of maximum tsunami wave pressure acting on the cuboid model
2) Tsunami wave force evaluation formulae using hydraulic quantity in a state with structures
Table 8.1.4-2 shows the maximum tsunami wave force based on tsunami wave force
Appendix 8 - 25

evaluation formulae and empirical results. Taking into account the Froude number time series
tsunami shapes where models were not set up and the time periods when there is no flow
velocity, t<10s is regarded as a non-steady state and t≥10s a quasi-steady state, and the
maximum tsunami wave forces were consolidated according to each state. Also, Figure 8.1.411 uses the example of a zero degree inclining cuboid to show the empirical results according
to a time series tsunami wave force acting on the cuboid and the results calculated using
tsunami wave force evaluation formula.
The features are shown below of each tsunami wave force evaluation formula, which havebeen obtained from the results of comparisons of these formulae.
• In a quasi-steady state (t≥10s), the tsunami wave force evaluation formulae presented by
Kihara et al. (2012) and Arimitsu et al. (2012) coincided approximately with the empiricalresults.
• In a non-steady state (t<10s), the tsunami wave force resulting from the evaluation formula
presented by Arimitsu et al. (2012) generally coincided with maximum tsunami wave force
in the experiments.
• The calculation formula presented by Kihara et al. (2012) was applicable during a quasisteady state, and in a non-steady state, a tsunami wave force was obtained depending on thecase that significantly surpassed the empirical results.
Table 8.1.4-2 Comparison of maximum tsunami wave force acting on the cuboid model
Unit: kN/m
Flow
type

Cuboidangle(degree)

type1

type2

type3

Maximum Tsunami wave force
Arimitsu et al. (2012)

Experiment

Kihara et al. (2012)

In a nonsteady state(t<10s)In a quasisteady state(t10s)In a nonsteady state(t<10s)In a quasisteady state(t10s)In a nonsteady state(t<10s)In a quasisteady state(t10s)

0

1.6

7.4

1.2

7.1

2.9

8.0

15

1.8

7.4

-

7.3

4.3

7.9

45

1.3

7.4

0.9

7.5

1.3

7.4

0

6.4

14.2

6.3

14.6

7.9

14.4

15

6.0

14.5

-

13.6

9.5

13.3

45

4.2

12.7
13.2

13.4

4.0
-

12.8

0.7

1.8
-

13.4

0
15

0.4

13.3

-

13.1

-

14.4

45

0.2

13.3

-

13.5

-

14.6

Appendix 8 - 26

13.9

20000Experiment
Kihara et al. (2012)
Arimitsu et al. (2012)

type1

F(N/m)

15000
10000
5000
0
0

20000

60

90
Time (sec)

5000

150

180

Experiment
Kihara et al. (2012)
Arimitsu et al. (2012)

type3
15000
F(N/m)

10000

120

20000

Experiment
Kihara et al. (2012)
Arimitsu et al. (2012)

type2

15000
F(N/m)

30

10000
5000

0

0
0

30

60

90
Time (sec)

120

150

180

0

60

120
180
Time (sec)

240

300

Figure 8.1.4-11 Comparison of time series of tsunami wave force acting on the cuboid model (Cuboid
angle: 0 degree)
8.1.4.4. Tsunami wave force calculations using calculation results from plane two-dimensional models(1) Examination overview
Focusing on tests for assessing tsunami wave force acting on cuboids (three-dimensional
structures), the tsunami wave force acting on the structure was calculated by finding theinundation depth and flow velocity at appropriate positions corresponding to tsunami wave force
evaluation formulae based upon numerical simulations using plane two-dimensional models that
focused on a non-steady state immediately after a tsunami arrives in front of a structure.
(2) Simulating conditions
Of the tests for assessing tsunami wave force acting on cuboids, the target experiments werecases where a cuboid model was set up at an inclination of zero degrees in a type 1 flow. Figure
8.1.4-12 shows the numerical experiment water route used for the numerical simulations with aplane two-dimensional model. Also, Table 8.1.4-3 shows the principle simulating conditions.
For the numerical simulations of tsunami, a method was used that differentiated thecontinuity equation and nonlinear long-wave theory equation by means of a staggered leapfrog
method. So that the conditions would be the same as the experiments, a storage portion and gate
Appendix 8 - 27

were simulated at the upstream boundary and the pass-through flow rate is given according to
Kuriki et al. (1996), and then, a movable weir was simulated at the downstream boundary andthe overflow rate was taken into consideration according to Honma et al. (1940) according to thetime variation for the crest height. With respect to the upstream boundary, the storage water levelin the storage portion was set at 4.0 m and the height of the gate opening at 0.1 m, because theflow rate per unit width was considered as a value that successfully reproduces the empiricalresults, based upon Kuriki et al. (1996), of the linear flow rate obtained from the inundation depth
and flow velocity at points H2 and V1.
(3) Calculation results
As for the calculation results using a plane two-dimensional model, Figure 8.1.4-13 shows
the time series tsunami shape for inundation depth and flow velocity. The features are given below
for the inundation depth and flow velocity in front of the model and at points H2 and V1.
• For the inundation depth at point H2, the empirical results and calculation results coincide
approximately, and the continuously high flow velocity, which was observed in the empiricalresults, was able to be reproduced for the flow velocity at point V1.
• The inundation depth in front of the model was shown to be twice that of the progressive wave
at point H2, depending upon the effect of the wave reflected from the model.
• The flow velocity in front of the model was shown to be a maximum of about 3 m/s
instantaneously when the tsunami arrived, but subsequently, the progressive wave andreflected wave overlapped, so the flow velocity became conspicuously lower.
(4) Tsunami wave force calculations using calculation results based upon plane two-dimensionalmodels
The calculation results from the plane two-dimensional model (inundation depth and flow
velocity) were used to calculate tsunami wave force. To calculate tsunami wave force, the tsunami
wave force evaluation formula presented by Arimitsu et al. (2012) was utilized. Figures 8.1.4-14
and 8.1.4-15 show the empirical results of a tsunami wave force time series and tsunami wave
pressure time series acting on a cuboid as well as the results calculated using the tsunami wave
force evaluation formula. The empirical results were calculated using the results for measurement
aspect 1, and the calculation results using the evaluation formula presented by Arimitsu et al.
(2012) utilize the hydraulic quantity in front of the model.
The features are given below for tsunami wave force and pressure as calculated using theevaluation formula presented by Arimitsu et al. (2012).
• In a non-steady state (t<10s), the maximum tsunami wave force according to the evaluation
formula presented by Arimitsu et al. (2012) was 1.7kN/m and the maximum tsunami wave
Appendix 8 - 28

force according to the experiments was 1.6kN/m, showing that these coincided approximately.
• The tsunami wave force according to the evaluation formula presented by Arimitsu et al.
(2012) showed the maximum value when the tsunami arrived, and although there was atendency for the tsunami wave force time series to somewhat exceed the empirical results, it
was able to be reproduced for the most part.
• The tsunami wave pressure distribution according to the evaluation formula presented by
Arimitsu et al. (2012) was not able to be reproduced up to a distribution having a local
maximum somewhat upward from the bottom surface as seen in the empirical results of t=2.0s
due to the characteristics of the evaluation formula.
Although the calculation formula presented by Arimitsu et al. (2012) was presented based
on, among other data, the results of numerical simulations for experiments using the dam-breakmethod, it was verified that the calculation formula was able to be applied to the estimation oftsunami wave force in a non-steady-state for the tsunami head, even in experiments that reproduce
tsunami on a scale close to an actual phenomenon.

～
～

4.2m
3.0m
1.5m

Upstreamboundary
Water
Gate
StrageArea
Tsunami

Y

H3
V1
H2

H4

Canal
gate

0.9m

V2

Front of cuboid model
21.8m

Cuboid model
Downstream(W×L×H: 1×1×2m) boundary

4.0m

X
0.9m

2.0m

10.7m

13.2m

: Outputting point of water level and flow velocity

Figure 8.1.4-12 The numerical experiment water channel used for the numerical simulations with aplane two-dimensional model

Appendix 8 - 29

Table 8.1.4-3 Simulating conditions used for the numerical simulations with a plane two-dimensional
model
Item

Setting value

Goverment

Nonlinear long-wave theory equation and continuity equation

equations

A storage portion and gate were simulated at the upstream

Upstreamboundary and the pass-through flow rate is given according toboundary

Kuriki et al. (1996)
A canal gate was simulated at the downstream boundary and theDownstream

overflow rate was taken into consideration according to Honma etboundaryal. (1940) according to the time variation for the crest height

Grid sizes

0.05m

Computation timeinterval
Simulating time

0.001s
25s

Manning’s
n=0.010m-1/3·s

coefficientof roughness

Front of cuboid model: Inundation depth

H2: Inundation depth

3.0
Experiment

2.5

Inundation depth (m)Inundation depth (m)3.0Calculation

2.0
1.5
1.0
0.5
0.0

Calculation

2.0
1.5
1.0
0.5
0.0

‐10

0

10

20
30
Time (s)

40

50

60

‐10

V1: Flow velocity

0

10

20
30
Time (s)

40

50

60

Front of cuboid model: Flow velocity

6.0

6.0

Flow velocity (m/s)

Experiment

5.0

Flow velovity (m/s)

2.5

Calculation
4.0
3.0
2.0
1.0

5.0

Calculation

4.0
3.0
2.0
1.0

0.0

0.0
‐10

0

10

20
30
Time (s)

40

50

60

‐10

0

10

20
30
Time (s)40

Figure 8.1.4-13 Time series of inundation depth and flow velocity

Appendix 8 - 30

50

60

5000
ExperimentF(N/m)

4000

Arimitsu et al. (2012)

3000
2000
1000
0
0

5

10
15
Time (s)20

25

Figure 8.1.4-14 Time series of tsunami wave force acting on the cuboid model
Experiment
0.5s
2.0s
3.0s
5.0s
7.0s
10.0s
5.625s

0.6
0.4

0.75s
2.0s
3.0s
5.0s
7.0s
10.0s
0.875s

0.8

z (m)

0.8

z (m)

Arimitsu et al. (2012)

1.0

1.0

0.6
0.4

0.2

0.2

0.0

0.0
0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

p/ρg (m)

0.4

0.6

0.8

1.0

p/ρg (m)Figure 8.1.4-15 Time series of tsunami wave pressure acting on the cuboid model
8.2. Calculation of sediment transport
8.2.1. Examples of calculation methods
8.2.1.1. Model presented by Fujii et al. (1998)(1) Friction velocity calculation formula
For calculation of friction velocity u*, Kobayashi et al. (1996) used a logarithmic law shownin the following equation that may be applied under tsunami.
However, in the area of narrowing, the effect of the pressure gradient accompanying flow
acceleration and deceleration makes the vertical distribution of current velocity uniform and thebottom shear stress increase, so Fujii et al. (1998) used a method for assessing bottom shear stressbelow the pressure gradient. u* is calculated using an equation where the log-wake law for current
velocity distribution is integrated in a vertical direction.
(2) Bed load equation
Kobayashi et al. (1996) used trap experiments to find an appropriate bed load transport
Appendix 8 - 31

equation coefficient where the bed load volume is proportional to the Shields number τ raised tothe power of 1.5. That was referenced when using the following equation for bed load transportvolume.
Q  80 1 .5 sgd 3

where, Q: bed load transport rate per unit width per unit time, τ: Shields number, s: underwater
density of sand, and g: acceleration of gravity.
(3) Consideration of suspended sediment
Models have been proposed that mix advection-diffusion and local flux, in which part of thetotal bed load transport rate behaves as a local flux governed primarily by external force at thelocation and the remainder behaves in accordance with the advection-diffusion equation for asingle layer as a suspended component. Although this model is incapable of considering up to
non-equilibrium relating to vertical distribution of the suspended sediment concentration, it ischaracterized by the capability to take into account non-equilibrium that emerges due to delay inthe total bed load transport rate flux following sudden changes in the external force.
8.2.1.2. Model presented by Takahashi et al. (1999)(1) Friction velocity calculation formulaAn evaluation is made based upon friction force according to Manning’s roughness
coefficient used in a non-linear longwave equation.
(2) Bed load equation, pickup rate equation, and deposition rate equation
Bed load transport volume Q, suspended sediment pickup rate E, deposition rate S are
expressed in the following formula.
Q  21 3 2 sgd 3

E  0.012 2 sgd  
S  wC  where, τ: Shields number, S: underwater density of sand, g: acceleration of gravity, d: sandparticle size, σ: sand density, w: sedimentation rate, and C : mean suspended sedimentconcentration.
(3) Consideration of suspended sediment
For the calculation of sediment transport, an equation of sediment transport continuity andan equation for sand volume exchanged between the bed load layer and suspended sand layer
will be used. Because this model does not assume an equilibrium state where pickup rate andAppendix 8 - 32

deposition rate are in balance, it may also be applied to suspended sediment conditions in nonequilibrium that occur due to non-steady dragging power.
8.2.1.3. Model presented by Ikeno et al. (2009)
The bed load equation differs from that of the model presented by Takahashi et al. (1999).
(1) Bed load equation: Ashida and Michiue (1972)
Q  17 sgd 3  1 .5 1   c /  1  u * c / u * 

where, Q: Bed load transport volume per unit width per unit time, τ: Shields number, S:
underwater density of sand, g: acceleration of gravity, d: sand particle size, τc: critical Shields
number, and u*c: critical friction velocity.
(2) Pickup rate equation
The calculation formula for dimensionless pickup rate is shown below.
E
0.2
1.6
2
 aP1 P2    c 
sgd

P1  / sgd3
P2  w /(sgd ) 0.5

where, a: coefficient, v: viscosity coefficient, and w: sedimentation rate.
When the sand particle size is 0.08mm and a=0.15, the pickup rate coefficient is 0.0056.
When the sand particle size is 0.2mm and a=0.15, the pickup rate coefficient is 0.015.
(3) Deposition rate equation
There are cases where the mean concentration and bottom concentration are used as theconcentration in the bed load deposition rate equation.
8.2.1.4. Model presented by Takahashi et al. (2011)
With respect to the pickup rate equation and bed load equation presented by Takahashi et al.
(1999), the hydraulic model experiments were conducted, and a model improved so that particle size
dependence is taken into account.
Hydraulic model experiments were conducted using sand having three different particle sizes
where the median diameters are 0.166mm, 0.394mm, and 0.267mm.

Appendix 8 - 33

(1) Bed load equation
Q  5 .6 1.5 sgd 3 ( d  0.166 mm )Q  4 .0 1.5 sgd 3 ( d  0 .267 mm )Q  2 .6 1.5 sgd 3 ( d  0 .394 mm )(2) Pickup rate equation

E  7.0  10 5 2 sgd   ( d  0.166 mm )E  4.4  10 5 2 sgd   ( d  0.267 mm )E  1 .6  10 5 2 sgd   ( d  0 .394 mm )8.2.2. Calculation example: Hachinohe port
8.2.2.1. Examination overview
Calculations were performed to reproduce sediment transport at Hachinohe port with regard to
the Chile tsunami on May 24, 1960. Two methods, one presented by Takahashi et al. (1999) and theother presented by Ikeno et al. (2009), were the methods used for calculation of sediment transport,
and calculations of three cases were performed, in which the upper concentration limit for suspended
sediment were set at 1%, 2% and 5%. For the coefficient presented by Ikeno et al. (2009), a was set at
0.15, and the volume concentration for the bottom was used when calculating the deposition rate.
8.2.2.2. Calculation region and modeling
The range analyzed in the numerical simulation was the region enclosed within the rectangle in
Figure 8.2.2-1 (range extending approx. 3.2 km east to west, and approx. 2.2 km north to south). A
diagram of the modeled water depths is given in Figure 8.2.2-2. Elevation data was input also for thegrids on land (water depth of 0 m or greater) at the point in time during the calculation initial period,
and run-up calculations performed. However, with respect to the grids on land at the point in time
during the calculation initial period, the calculations were performed with a configuration where only
deposits resulted but erosion did not when sediment transport was calculated.

Appendix 8 - 34

Minato tide gauge station

Figure 8.2.2-1 Analysis area

Figure 8.2.2-2 Analysis area (i, j are grid number.)Appendix 8 - 35

8.2.2.3 Calculation conditions
Table 8.2.2-1 shows calculation condition list of tsunami numerical simulation and calculating
the sediment transport.
Table 8.2.2-1 Calculation conditions list
Parameter

Calculation conditions

Computational Region

Around Hachinohe Port (range extending approx. 3.2 km east to west,
and approx. 2.2 km north to south)

Grid sizes

10.3m

Computation time interval

0.45 seconds

Fundamental equation of fluid

The Nonlinear Shallow Water Wave

Simulating time

10 hours

Land side boundary condition

Considering run up

Offshore side boundary
condition

Input the waveform of the neighborhood of breakwater tip
The tide level is T.P.±0.0m

Bottom friction

Roughness coefficient of Manning: n=0.03m-1/3s

Horizontal eddy viscosity
coefficient

10m2/sParticle size

0.26mmDensity of sand

2,675kg/m3

Porosity

0.4

Sedimentation rate

0.035m/s(Rubey, 1933)

8.2.2.4. Offing boundary conditions
For the offing boundary conditions pertaining to tsunami height, the water level in Figure 8.2.24 is given within the range indicated by the arrow in Figure 8.2.2-3. In order to verify the
reproducibility of tsunami height calculations, a comparison was conducted of the time waveforms in
tidal observation records (Japan Meteorological Agency) and calculated results at Minato tide gauge
stations (Figure 8.2.2-5).

Appendix 8 - 36

Land side boundary condition
Offshore side boundary condition

Minato tide gauge station

Figure 8.2.2-3 The offshore side boundary where the time waveform was input (i, j are grid number)

Figure 8.2.2-4 Time waveform of incident tsunami

Figure 8.2.2-5 Comparison of calculation results and tide gauge records (Japan Meteorological
Agency)8.2.2.5. Observed values
In order to verify the distribution map for variation in the sea bottom topography change withnumerical simulations, observation data (Figure 8.2.2-8) of variation in the sea bottom topographychange using depth maps before and after the tsunami strike (Figure 8.2.2-6 and 8.2.2-7) was prepared.

Appendix 8 - 37

Figure 8.2.2-6 Bathymetry before and after the Chilean Tsunami's strike -back of port- (Left: April
1960, Right: June 1960)

Figure 8.2.2-7 Bathymetry before and after the Chilean Tsunami's strike -mouth of port- (Left: April
1960, Right: June 1960)
Source: Ministry of Transport (1961)

Figure 8.2.2-8 Topography changes created from sounded data (i, j are grid number)
Appendix 8 - 38

8.2.2.6. Examination results(1) Qualitative evaluation using distribution map
Figures 8.2.2-9 to 8.2.2-14 show distribution maps of the final extent of topography change.
There are six calculation cases:
Takahashi et al. (1999)
upper concentrations of suspended sediment: 1%, 2%, and 5%
Ikeno et al. (2009)
upper concentrations of suspended sediment: 1%, 2%, and 5%
As presented by Ikeno et al. (2009) a is 0.15 (Y=aX2).
From a comparison of the observed values and a map showing the distribution of the final
topography change, it may be said that the trends in sea bottom topography change were able tobe reproduced well through measurements of erosion at the harbor entrance, small deposits at
branch points, and deposits at the innermost part of the harbor. Little differences were foundbetween Takahashi et al. (1999) and Ikeno et al. (2009), and both models provided good
reproductions of the extent of sea bottom topography change where the upper concentration limit
for suspended sediment were between 1% and 2% and found that 5% was an overestimate.
With respect to Ikeno et al. (2009), the maximum values for topography change where theupper concentration limit for suspended sediment was 2%, which the reproducibility was good,were found near the harbor entrance, and the maximum value for sediment was 8.4 m and the
maximum value for erosion was 6.5 m (Figure 8.2.2-15).

Appendix 8 - 39

*i,j are grid number

Figure 8.2.2-9 Distribution maps of the final

Figure 8.2.2-12 Distribution maps of the final

extent of topography change Takahashi et al.

extent of topography change
Ikeno et al. (2009)
a=0.15(Y=aX2) Upper concentration limit(1999)
Upper concentration limit for suspended

for suspended sediment 1%

sediment 1%

Figure 8.2.2-10 Distribution maps of the final

Figure 8.2.2-13 Distribution maps of the final

extent of topography change
Takahashi et al. (1999)
Upper concentration limit for suspended

extent of topography change
Ikeno et al. (2009)
a=0.15(Y=aX2) Upper concentration limit

sediment 2%

for suspended sediment 2%

Figure 8.2.2-11 Distribution maps of the final

Figure 8.2.2-14 Distribution maps of the final

extent of topography change
Takahashi et al. (1999)
Upper concentration limit for suspended

extent of topography change
Ikeno et al. (2009)
a=0.15(Y=aX2) Upper concentration limit

sediment 5%

for suspended sediment 5%
Appendix 8 - 40

Figure 8.2.2-15 The maximum amount of sediment, erosion (Ikeno et al. 2009)
a=0.15(Y=aX2) Upper concentration limit for suspended sediment 2%*i, j are grid number(2) Quantitative evaluation of sediment and erosion volume
The harbor interior was partitioned into four regions (Figure 8.2.2-16), and the sedimentvolume and erosion volume were calculated for each region. In the region enclosed within therectangle in Figure 8.2.2-16, the sediment volume and erosion volume were calculated only forthe grids set in the sea area during the calculation initial period.
Of the four regions, the results of a comparison with observation data for the regions otherthan part 3 showed that reproducibility was good for the upper concentration limit for suspended
sediment from 1% to 2% for both Takahashi et al. (1999) and Ikeno et al. (2009), and it was foundthat 5% would result in an overestimation (Figures 8.2.2-17 to 8.2.2-20, Table 8.2.2-2, and Table
8.2.2-3).

Figure 8.2.2-16 Division of the domain that calculated amount of sediment, erosion

Appendix 8 - 41

1) Takahashi et al. (1999)

Figure 8.2.2-17 Amount of sediment per domain (Takahashi et al., 1999)

Figure 8.2.2-18 Amount of erosion per domain (Takahashi et al., 1999)
Table 8.2.2-2 Amount of sediment and erosion per domain (Takahashi et al., 1999)
Upper concentration limit for suspended sediment1%

domain2%

Observation

5%

Sediment

ErosionSediment

ErosionSediment

ErosionSediment

Erosion

(m3)

(m3)

(m3)

(m3)

(m3)

(m3)

(m3)

(m3)

part1

2.7E+04

1.4E+03

5.0E+04

1.7E+03

9.5E+04

1.5E+03

3.9E+04

2.9E+04

part2

2.2E+04

2.4E+04

3.0E+04

2.9E+04

4.2E+04

3.5E+04

3.5E+04

3.2E+04

part3

3.8E+04

8.6E+04

4.2E+04

1.7E+05

4.8E+04

2.4E+05

-

-

part4

4.3E+04

1.3E+05

6.4E+04

2.5E+05

7.2E+04

5.7E+05

6.4E+04

1.4E+05

Total

1.3E+05

2.5E+05

1.8E+05

4.5E+05

2.6E+05

8.4E+05--

9.2E+04

1.6E+05

1.4E+05

2.8E+05

2.1E+05

6.0E+05

1.4E+05

2.0E+5

total(part3 is
excluded)Appendix 8 - 42

2) Ikeno et al. (2009)

Figure 8.2.2-19 Amount of sediment per domain (Ikeno et al., 2009)

Figure 8.2.2-20 Amount of erosion per domain (Ikeno et al., 2009)
Table 8.2.2-3 Amount of sediment and erosion per domain (Ikeno et al., 2009)
upper concentration limit for suspended sediment1%

domain2%

Observation
5%

Sediment

ErosionSediment

ErosionSediment

ErosionSediment

Erosion

(m3)

(m3)

(m3)

(m3)

(m3)

(m3)

(m3)

(m3)

part1

2.7E+04

1.8E+03

4.5E+04

2.4E+03

8.9E+04

2.3E+03

3.9E+04

2.9E+04

part2

2.9E+04

1.9E+04

4.3E+04

1.7E+04

6.3E+04

2.6E+04

3.5E+04

3.2E+04

part3

5.1E+04

1.0E+05

6.8E+04

1.3E+05

6.8E+04

2.3E+05

-

-

part4

7.2E+04

2.4E+05

1.0E+05

2.6E+05

1.2E+05

4.9E+05

6.4E+04

1.4E+05

Total

1.8E+05

3.6E+05

2.6E+05

4.1E+05

3.4E+05

7.5E+05--

1.3E+04

2.6E+05

1.9E+05

2.8E+05

2.8E+05

5.2E+05

1.4E+05

2.0E+5

total(part3 is
excluded)Appendix 8 - 43

8.2.2.7. Friction velocity and Shields number
The friction velocity and Shields number are given below for a case of Ikeno et al. (2009) where
the upper concentration limit for suspended sediment is 2% and a=0.15.

u* spatial mean maximum value: 13.7
Routh number ( u* / ws ): 3.9
where, ws: sedimentation rate (particle size: 0.26mm, and calculated according to Rubey(1933)).
Spatial average of the Shields number: 1.14
Spatial average maximum value of the Shields number: 7.84
8.2.2.8. Summary• Calculations were performed to reproduce topography change at Hachinohe port during the 1960
Chile tsunami.
• The simulation focused on Takahashi et al. (1999) and Ikeno et al. (2009), and both models wereable to reproduce trends where occurred at the harbor entrance and sedimentation was depositedat the innermost part of the harbor. There were little differences between the two models.
• Both models provide a good reproducibility of a case where the upper concentration limit forsuspended sediment was between 1% and 2%, and 5% resulted in an overestimate.
8.2.3. Examples and previous research on damage related to sediment transport
8.2.3.1. Examples of scouring phenomena during the 2011 Tohoku tsunami
Case studies from the following material were consolidated of damage from scouring and otherphenomena around buildings and structures along the coastline due to sediment transport that occurred
during the 2011 Tohoku tsunami.
• Port and Airport Research Institute, National Institute for Land and Infrastructure Management,
and Fisheries Research Agency, “Report of Investigation of Earthquake and Tsunami Damage to
Ports, Harbors, Airports and Fishing Ports Due to the Great East Japan Earthquake”, TechnicalLectures on Ports, Harbors, Airports and Fishing Ports, May 2011.
• 2011 Great East Japan Earthquake Tsunami Joint Survey Group Report Meeting, July 2011.
• Great East Japan Earthquake Report Meeting, 2.4 Sea Coast, Characteristics of Damage to
Coastal Structures and Hinterland from Tsunami (National Institute for Land and InfrastructureManagement, Ministry of Land, Infrastructure, Transport and Tourism), April 2011

Appendix 8 - 44http://www.nilim.go.jp/lab/bbg/saigai/h23tohoku/• 2011 Report on Investigation of Great East Japan Earthquake Damage (Building ResearchInstitute)
http://www.kenken.go.jp/japanese/contents/topics/20110311/0311report.html• Disaster Prevention Working Group, Ports Subcommittee, Council for Transport Policy under the
Ministry of Land, Infrastructure, Transport and Tourism, “Comprehensive Approach to Tsunami
Countermeasures for Harbours and Ports (Interim Report)”, July 2011.
• Disaster Prevention Working Group, Ports Subcommittee, Council for Transport Policy under the
Ministry of Land, Infrastructure, Transport and Tourism, “Approach to Tsunami
Countermeasures for Harbours and Ports”, June 2012.
(1) Investigation results
1) Examples of damage
Tomita (2011) and Sugano (2011) reported cases of damage that included scouring along
the coastline (Hachinohe port), damage to corners of sheet pile-type quays and damage tostraight portions of sheet pile-type quays (Soma port), and damage to corners of gravity-type
quays (Hitachi port section of Ibaraki port), and that the damage increased due to theoverlapping of ground motion, liquefaction, damage to pavement and sheet piles, scouring,differential water pressure, and tsunami wave pressure.
Takahashi (2011) presented the example of Hachinohe port where it has been estimatedthat a 6m high tsunami struck. More specifically, Takahashi (2011) reported that the fast flowof the tsunami caused about 10m of scouring on corners of wharves and at the breakwater
opening. Also, the overturning of a caisson, which formed the corner of reclaimed land, wasreported to be due to scouring along the sea bottom in front of the caisson.
Sakakiyama et al. (2011) reported examples of scouring that occurred behind sea
embankments.
Suwa (2011) verified that, with regard to coastal structures along the coasts of Miyagi
Prefecture and Iwate Prefecture, the significant overflow of embankments was also due to adamage to the embankments as well as topography change behind the embankments, and theoverflow reached several meters, but Suwa reported three cases of damage to embankments:
complete destruction of the embankments, scouring of the back slope and partial rupture onlyof the damaged crest, and no damage to the main embankment unit.
Building Research Institute (2012) found many traces of large holes due to scouring as
the strong current acted on corners of structures during tsunami action, and that the scouring
caused buildings to collapse and tilt, and the tsunami produced intense scouring that exposed
many footings and pile heads.
Appendix 8 - 45

2) Failure mechanisms
The Ministry of Land, Infrastructure, Transport and Tourism (2011) and Ministry of Land,
Infrastructure, Transport and Tourism (2012) compiled mechanisms of how breakwaters andseawalls failed as well as how future countermeasures should be approached. With regard to
breakwater failure mechanisms, these reports used the example of breakwaters at the entranceof Kamaishi port, and pointed out that, among other events, the caissons slid due to thedifference in water levels outside and inside the port, foundation mounds were scoured due tothe strong flow created by the water level difference, and caissons subsided and slid down.
With regard to seawalls, these reports stated that there were many examples where overflow
during leading waves scoured back slopes and slope toes resulting in collapses.
(2) Summary•

Examples were observed where the faster flow caused by the tsunami produced relatively
extensive scouring on the corners of wharves and at breakwater openings.

•

Examples were observed where scouring in front of corners of reclaimed land resulted incaissons overturning.

•

At breakwaters, scouring of foundation mounds, which resulted from the strong flow
produced by differences in water levels, occurred along with caissons sliding due to waterlevel differences as well as caissons subsiding and sliding down.

•

At seawalls, many examples were observed where overflow during the leading wave causedscouring of back slopes and slope toes, resulting in collapse.

•

At revetments and other similar structures, cases were also observed where the leading wave
damaged weak parts of structures and the backwash increased the damage at such locations
as well as other examples where damage was sustained due to the action of the external force
from both leading waves and backwash. Seismic ground motion, liquefaction, tsunami wave
pressure, and scouring overlapped, increasing the damage.
Around buildings, many traces have been observed where, during the tsunami action, strong
currents acted on corners and the scouring resulted in large holes. Situations resulted inbuildings collapsing and tilting into holes created by the scouring. In addition, intensescouring, caused by the tsunami, exposed many footings and pile heads.

8.2.3.2. Previous studies on scouring(1) Evaluations of scouring around buildings due to tsunami
There is an empirical formula presented by Noguchi et al. (1997), which is shown below,that serves as a formula for assessing scouring around structures. Noguchi et al. (1997) defined
Appendix 8 - 46

the various quantities related to scouring as shown in Figure 8.2.3-1, and the magnitude of thestanding vortex and the scouring depth are almost equal, so the scouring depth has been estimatedby finding the magnitude of the standing vortex.
R  g 1 4 q 1 2 z f

14

where, R: scouring depth (m), g: acceleration of gravity (m/s2), q: flow rate of falling water(m3/m/s), and zf: height from water level in front of revetment to crest of revetment (m).
Of the proposals for reasonably assessing the damage to land structures resulting fromtsunami, Yamamoto et al. (2011) conducted multiple hydraulic model experiments with hydraulicmodels in order to develop a practical numerical prediction model for scouring of the lower partof revetments due to return flow, and thereby increase the understanding of scouring mechanisms
and Yamamoto et al. (2011) proposed a method for assessing the maximum scouring depth andits position. Yamamoto et al. (2011) stated that the distance up to the location of maximum
scouring is able to be found if the calculated value for parabolic movement is corrected using thepeak current velocity of the return flow, and that the maximum scouring depth may be calculated
by using the cumulative value for the vertical direction compound of motion energy or impulse
per unit width of the returning flow water mass up to the peak current velocity.
FEMA (2012) is shown in Table 8.2.3-1 as the relationship between inundation depth andscouring depth according to Dames and Moore (1980). In keeping with the distance from thecoastline and bottom material, the scouring depth is expressed as a percentage of the inundation
depth. For example, in a case where the bottom material is loose sand and the inundation depth
is 10m at a distance of 90m or more from the coastline, the scouring depth is calculated to be 6m.
Arikawa et al. (2014) used hydraulic model experiments to examine the extent of scouring
behind a vertical embankment when a tsunami overflows the embankment. Arikawa et al. (2014)
showed that overflow depth and scouring depth are in a highly correlated proportional
relationship, and may be quantitatively assessed by means of a similarity law commensurate withthe sedimentation rate (Figure 8.2.3-2).
(2) Examinations using numerical analysis
Goto et al. (2013) used a particle method-type numerical wave tank that allowed for thesimplified treatment of moving bed boundaries interlinked with flow fields as well as the tracking
in a Lagrange manner of the movement of caissons, covered blocks and mound rubble so as toconduct numerical simulations of the process of failure due to overflowing and scouring ofcomposite breakwaters. The water level outside the harbor was held constant and the water level
inside the harbor varied to compare failure processes, and in the case where the water level inside
Appendix 8 - 47

the harbor was the lowest, the tsunami wave force caused caissons to slip before scouring
occurred. In cases where the water level inside the harbor was somewhat high, it was confirmedthat breakwaters failed due to the increased size of scouring holes, and in cases where the waterlevel inside the harbor was the lowest and the levees had been widened, caisson movement was
effectively suppressed and failure did not result.
Nakamura et al. (2015) focused on coastal embankments damaged due to the tsunami
resulting from the 2011 Tohoku tsunami, and utilized actual scale numerical analysis to examine
mechanisms of scouring development and the effectiveness of measures to counter scouring. The
model, which was used in this study for performing numerical simulations of three-dimensional
fluid, structures, topography change, and ground coupling, was comprised of a main solver thattook into account changes in topography to analyze fluid motion in all gas-liquid phases
comprised of incompressible fluid including fluid inside the gaps of moving beds, as well as amodule based upon the VOF method for tracking the air liquid surface, a module for calculating
topography change due to bed load and suspended sediment transport and analyzing the
distribution of suspended sediment concentrations, and other modules (Nakamura et al., 2013;
Nakamura and Mizutani, 2014).

Figure 8.2.3-1 The various quantities related to scouring (Noguchi et al., 1997)
Table 8.2.3-1 Approximate scour depth as a percentage of inundation depth, d (Dames and Moore,
1980)

Loose sandScour depth (% of d)(Shoreline Distance < 300 feet)80

Scour depth (% of d )(Shoreline Distance > 300 feet)
60

Dense sand

50

35

Soft silt

50

25

Stiff silt

25

15

Soft clay

25

15

Stiff clay

10

5

Soil type

Appendix 8 - 48

Figure 8.2.3-2 Relationship between overflow depth and scouring depth (Arikawa et al., 2014)

8.2.3.3. Previous studies on upper concentration limit for suspended sediment
When calculating bottom shear stress, the sediment transport calculation model presented by
Takahashi et al. (1999) tends to overestimate bottom shear stress as total water depth is reduced. As
bottom shear stress increases, lifting sand is supplied to the suspended sediment layer, and theconcentration of suspended sediment increases. When calculating the pick-up rate and concentrationof suspended sediment of these, it is ideal to use a model that takes into account physical mechanisms,
but currently, methods that set an upper concentration limit for suspended sediment and restrain theoverestimation of the volume of pick-up rate are often used.
With regard to the upper concentration limit for suspended sediment, there are cases where actual
scale verification has been performed using actual measured values of the sea bottom topographychange in harbors and ports during the Chile tsunami and the 2011 Tohoku tsunami in Tamada et al.
(2009), Fujita et al. (2010), Kondo et al. (2012), Morishita et al. (2014) and other studies.
Tamada et al. (2009) calculated sediment transport in the sea bottom topography change of
Kesennuma bay in Miyagi Prefecture at the time of the 1960 Chile tsunami, and conducted aparametric study of the calculation model grid size, particle size, and upper concentration limit forsuspended sediment. With the exception of the maximum depth when the particle size was 0.001 mm,a trend was observed where the calculation results of cases where the upper concentration limit forsuspended sediment was 5% showed a greater maximum depth and sediment deposit depth than the
Appendix 8 - 49

results of calculations in a case where the concentration was 1%. Also, in a case where the particle
size was 0.1 mm and the grid size 5 m, it was confirmed that there was a tendency to overestimate
depth to be greater than the actual values when the upper concentration limit for suspended sediment
was 5%. Based on these facts, it has been surmised that the upper concentration limit for suspended
sediment in Kesennuma bay during the 1960 Chile earthquake tsunami was less than 5%.
Fujita et al. (2010) conducted an examination of sea bottom topography changes of Hachinohe
port at the time of the 1960 Chile tsunami and conducted parametric studies of upper concentration
limits for suspended sediment of 1%, 2%, and 5% using a particle size of 0.21 mm and a calculation
model grid size of 10.3 m. The amount of topography change of each region (sediment volume anderosion volume) was tabulated and compared with the observed values, which showed that there wasgood reproducibility when the upper concentration limit for suspended sediment was set at 1% and2%, and it was confirmed that an overestimate would result using a concentration limit of 5% (Figure
8.2.3-3).
Kondo et al. (2012) calculated sediment transport in the sea bottom topography change at Miyako
port during the 2011 Tohoku tsunami. The examination was conducted using a particle size of 0.08mm, an upper concentration limit for suspended sediment of 1%, and calculation model grid size of
10 m, and confirmed that the model presented by Takahashi et al. (1999) was able to reproduce with
sufficient precision the actual topography change (Figure 8.2.3-4).
Morishita et al. (2014) calculated sediment transport in the sea bottom topography change of
Kesennuma bay during the 2011 Tohoku tsunami, deduced four factors that predominantly contributed
to sand movement (dimensionless dragging power, sediment transport equation coefficient, upper
concentration limits for suspended sediment, and sedimentation rate), and modified the model. The
upper concentration limit for suspended sediment should, intrinsically, be expressed as a function of
the friction velocity, so the upper concentration limit for suspended sediment was set so that it varies
according to current velocity. As for the factors other than upper concentration limit for suspended
sediment, these were set along with modifying the sediment transport equation coefficient anddimensionless dragging power to significantly improve the distribution of sand movement from theport entrance across narrow segments, and results were obtained that dramatically increased thesedimentation rate, approaching the actual sedimentation rate.
Sugawara and Takahashi (2014) focused on topography change of the Sendai plain due to the2011 Tohoku tsunami, conducted a numerical simulation using a method that utilized the coefficientsfor pick-up and bed load sediment, which were found using Takahashi et al. (2011) with the method
presented by Takahashi et al. (1999), and verified its applicability for calculating topography change
due to the 2011 Tohoku tsunami. A comparison was conducted of calculated results and observed
values for a vertical cross-section, and it was verified that the calculation was able to provide a good
reproduction of the behind seawalls and sandbars. On the other hand, in order to use calculations toAppendix 8 - 50

reproduce and deposits with regard to coastal forests, there are still issues in that it is necessary to take
into account spatial and temporal changes in the roughness coefficient, and further research is neededon model parameters for applying the sediment transport model to tsunami deposits thinner than 30
cm that are inland.
Sugawara et al. (2014) conducted an examination of topography change of the Sendai plain due
to the 2011 Tohoku tsunami. Multiple parametric studies, which included particle size, upper
concentration limits for suspended sediment, and other elements, were conducted by using thecoefficients for pick-up and bed load sediment, which were found using Takahashi et al. (2011) withthe method presented by Takahashi et al. (1999). In addition to a basic setting of 2% for the upper
concentration limit for suspended sediment, the examination reviewed limits of 1% and 4%.
Yamashita et al. (2015) performed empirical calculations using the method presented by
Takahashi et al. (2011) to examine topography change in Rikuzentakata city due to the 2011 Tohoku
tsunami. The upper concentration limit for suspended sediment was set using a relational expressioncommensurate with current velocity and water depth just as was presented by Imai et al. (2015) (frominterview with the authors). The calculation results captured well the distribution trend of and sedimentthat emerged in the results of field investigations and were able to provide good reproductions of the
distribution trends of sediment in sea areas for the extent of topography change, inundation height andthe process of tsunami run-up (Figure 8.2.3-5). The calculations for the extent of topography change
showed that there was of 2.1×106m3 , which was about the same level as the results of field
investigations (1.9×106m3).
Imai et al. (2015) performed numerical calculations using the method presented by Takahashi etal. (2011) to examine topography change in the vicinity of the mouth of the Kitakami river due to the2011 Tohoku tsunami, and was able to reproduce, for the most part, topography change of cultivatedagricultural land (Figure 8.2.3-6). For the upper concentration limit for suspended sediment, asaturated suspended sediment concentration formula was adopted, which is shown below and varies
according to the flow conditions according to Sugawara et al. (2014).


4



1


 s  w  h 3 ws
Cs 
 1

2 3
 s   w  es n uwhere, ρs: sand density (kg/m3), ρw: water density (kg/m3), h: water depth, ws: sand sedimentation rate(m/s), u: cross-sectional mean current velocity including sand (m/s), n: Manning’s roughness
coefficient (m-1/3·s), and es: pick-up efficiency.
The configuration when sediment transport was calculated in the previous studies discussed so
far regarding the concentration of suspended sediment in seawater during a tsunami have been
consolidated in a table (Table 8.2.3-2).

Appendix 8 - 51

Sediment volume (m3)Erosion volume (m3)Topography change (m)Topography change (m)Topography change (m)Topography change (m)Figure 8.2.3-3 Total result of topography changes per domain (Fujita et al., 2010)

Figure 8.2.3-4 Topography changes of representative cross section (Kondo et al., 2012)

Appendix 8 - 52

(a) Field survey results (survey in May 2011) (retouch figure by Kato et al., 2012)(b) Result of calculation

Figure 8.2.3-5 Comparing results of topography changes (Yamashita et al., 2015)

Appendix 8 - 53

* Add the range of the dashed line frame to a figure of Imai et al. (2015)
Figure 8.2.3-6 Maximum topography change distribution around the Kitakami River estuary (Imai etal., 2015)

Appendix 8 - 54

Table 8.2.3-2 Previous studies on upper concentration limits for suspended sedimentCalculation
grid intervals

Upper
concentration
limits for
suspended
sediment

literature

Real scaleverification

Sand particle
size used for
calculation

Takahashi et al.
(1999)

Kesennuma Bay*1

0.2mm

25m

-

Tamada et al.
(2009)

Kesennuma Bay*1

0.001mm-1mm

25m,5m1%,5%There was a tendency to overestimate depth to be greater than the actual values when
the upper concentration limit for suspended sediment was 5%.

Fujita et al.
(2010)*1

Hachinohe Port

0.26mm10.3m

1%,2%,5%There was good reproducibility when the upper concentration limit for suspended
sediment was set at 1% and 2%.
An overestimate would result using an upper concentration limit for suspended
sediment of 5%.

Kondo et al.
(2012)

Miyako Port*2

0.08mm

10m

1%

The model presented by Takahashi et al. (1999) was able to reproduce with sufficientprecision the actual topographical change.

Description on upper concentration limits for suspended sediment-

Appendix 8 - 55

  U 2 V 2

Morishita et al.
(2014)

Kesennuma Bay*1

0.3mm

10m

1%
Variable

Sugawara and Takahashi(2014)

Sendai Plain
AroundNatoriRiver*2

0.25mm-1%

A comparison was conducted of calculated results and observed values for a verticalcross-section, and it was verified that the calculation was able to provide a good
reproduction of the behind seawalls and sandbars.

Sugawara et al.
(2014)

Sendai Plain*20.166mm0.267mm0.394mm

Minimum:5m

1%,2%,4%The parameter study that changed sand particle size and suspended sedimentconcentration limits was carried out, and topography change was reproduced wellwhen an upper concentration limit for suspended sediment was set in 2%.

Yamashita et al.
(2015)

Rikuzentakata City
Hirota Bay*2

0.267mm-

Variable

A tendency of the topography amount of change was reproduced well.
By the method of Takahashi et al. (1999), pick-up is remarkably excessive, and the
reproduction of the topography change is difficult.

0.166mm0.267mm0.394mm

Minimum:5m

Variable

Topography change was reproduced well, by using the numerical simulation modelthat upper concentration limit for suspended sediment was set by a function dependingon the current velocity and the water depth.

Imai et al.
(2015)

Kitakami Rive
*2

U and V are average current velocity(m/s)
When current velocity was 10m/s, α was set with 0.01 so that upper concentration limit
for suspended sediment became 0.1.

*1: Topography change caused by the 1960 Chile tsunami, *2: Topography change caused by the 2011 off the Pacific coast of Tohoku Earthquake tsunami.

8.3. Evaluation of debris
8.3.1. Specifics of equations for calculating the impact force attributable to debris
Table 8.3.1-1 shows a classification of previously proposed equations for calculating the impact
force of debris.
Table 8.3.1-1 Classification of equations for calculating the impact force of debris
Author name

Type ofEquations of impact force of tsunami debris

debrisMatsutomi et al.
(1999)

Wood(Cylinder)Fm /(D 2 L)  (1.2～1.5)CMA v A0 /( gD)0.5

 ( / L)
1.2

0.4

f

Fm: Impact force, γ: Unit weight of drift wood, D: Diameter of wood, L: Length of wood,g: Acceleration of gravity, CMA: Apparent mass coefficient (Considering bufferingfunction of water), vA0: Impact velocity, σf : Yield stress of wood
Ikeno and Tanaka(2003)

Wood(Cylinder,
Prism,
Sphere)Japan Road
Association(2012)

Drift wood,
etc.

FEMA
(2012)

Wood
Container

FH /( gM )  S･CMA･ VH /( g 0.5 D 0.25 L0.25 )2.5

FH: Impact force, g: Acceleration of gravity, M: Weight of debris, S: Coefficient (=5.0),
CMA: Added-mass coefficient, VH: Velocity of debris, D: Diameter of debris (In case of arectangular column, the square section side length), L: Length of debris

P  0 .1Wv
P: Impact force, W: Weight of transport object, v: Surface flow velocity

Fi  1.3umax kmd (1  c)
Fi: Impact force, c: Added-mass coefficient, umax: Maximum flow velocity of the fluid,
md, k: Mass and effective stiffness of debris

Mizutani et al. (2005)

Container

 WV 
Fm  2wm BcVx2   x  , Vx ≒ C x  2 g m
 gdt Fm: Impact force, g: Acceleration of gravity, W: Weight of container, Bc: Width of container,ηm: Maximum water level of run-up tsunami, dt: Impact time, ρw: Density of water, Vx:
Drifting container velocity, Cx: Flow velocity of run-up tsunami
Arikawa andWashizaki (2010)

Container
Drift wood

2
6
m1 m 2(1   ) ~ 5 ~ 5 5 4 a 1k mF   p 5  m
 v
E ,3 k1  k2 ,m1  m 2
4 
,
3

2

a: One half of radius of impact surface (Here, it is 1/4 of the average of the longitudinaland lateral lengths of the container impact surface), E: Young's modulus of concrete, υ:Poisson ratio, m: mass, v: Impact velocity, γp: Energy damping effect by plastic, Subscript
1: Collision body, Subscript 2: Colliding body
Japan Bridge
Engineering Center(1978)

Ship

WV2
4gD
F: Impact force, W: Weight of impact ship, V: Impact velocity, D: Stopping distance of
impact shipF

Appendix 8 - 56

8.3.2. Verification of the validity of impact force calculation formulae
8.3.2.1. Examination overview
Using the results of hydraulic model experiments for large debris based upon Takabatake et al.
(2015), an examination was conducted on the applicability of previous impact force calculation
formulae and the properties of impact force. Aerial experiments and underwater experiments wereused for the examination which focused on logs and automobiles as the debris.
8.3.2.2. Experiment overview(1) Debris
For the debris, in addition to three types of logs, which are given in Table 8.3.2-1, thesubcompact automobile, which is shown in Figure 8.3.2-1, was used.
Table 8.3.2-1 Debris using for experiment (log)
Type
Cedar
Pine

Length1m
2m
2m

Diameter
0.380m
0.435mMass

Modulus of elasticity

72kg

9.1 kN/mm2

155kg~158kg

11.2 kN/mm2

178kg~181kg

Specifications
Length: 3,925mm
Width: 1,395mm
Height: 1,475mm
Mass: 320kg
Remarks: Engine and glass which do not
influence the strength areremovedFigure 8.3.2-1 Debris using for experiment (car) (A simple configuration of Takabatake et al (2015))(2) Measurement of impact force
For the experiment, the reactive force was measured by using steel plates to which steel rods
were attached that were capable of measuring axial strain. To convert the reactive force to impact
force, first, aerial experiments were conducted to find the inertial force (impact force) of an
impactor by means of an accelerometer attached to the impactor (debris), and next, the conversion
Appendix 8 - 57

coefficient was obtained between the inertial force and reactive force for the steel plate so as tocalculate the impact force during underwater experiments.
(3) Empirical results
1) Aerial experiments
The distinctive features of impact force of debris during the aerial experiments are given
below.
• The impact force of logs (wood) increased linearly vis-a-vis the impact velocity, andthere was a trend whereby the smaller the impact angle (angle formed by the steel plate),
the smaller the impact force (Figure 8.3.2-3).
• The impact force of automobiles was 1/10 or less than that of logs, and the impact force
increased linearly at impact velocities between 0.2m/s and 0.4m/s (Figure 8.3.2-5).
2) Underwater experiments
The distinctive features of impact force during the underwater experiments are given
below.
• The relationship between the impact velocity and impact force of logs (wood) is different
from the trend observed during aerial experiments (Figure 8.3.2-4).
• The impact force of automobiles increased almost linearly with respect to the impact
velocity, and if the storage water level was the same, the impact velocity or impact force
would increase at the higher initial water level (Figure 8.3.2-5).
• As for the effect of water when debris strikes a structure, almost no additional mass effect(effect of impact force increase) was observed, and there were many cases where acushion effect (effect of impact force decrease) was noticeably apparent (Figure 8.3.22).

Water cushion effect
クッション効果(Decrementof impact force)
Impact
衝突体（衝突力減少）Additional mass effect
付加質量効果(Incrementof impact force)（衝突力増大）Impactobjecthh

衝突体
object

The distanceis long, compared with
衝突体のスケールに
scale of比して離間距離が長い
impact objects.

The distanceis short, compared with
衝突体のスケールに
scale of impact
objects.
比して離間距離が短い

Figure 8.3.2-2 The effect of water when the debris impacts with a structure

Appendix 8 - 58

8.3.2.3. Impact force attributable to logs (wood)
The results of aerial experiments and underwater experiments were used to examine theapplicability of previous impact force calculation formulae.
(1) Physical properties of logs
The physical properties of logs were examined for both cases where previous settings(catalog values) were used, and cases where actually-measured physical properties were used
(Table 8.3.2-2).
Table 8.3.2-2 Physical property values of logs
(1) Previous settings (catalog values)
Modulus ofelasticity*1
E (kN/mm2)

Diameter
D(m)

Cedar

7.1

0.380

Pine

11.0

0.435

Length
L(m)

Mass
m(kg)

Densityρ(kg/m3)

2.0

156

687.8

1.0

72

634.9

2.0

179

602.3

Effective stiffness*2

k(kN/m)

2.4×103*1: Shimazu et al. (2001)*2: FEMA (2012)(2) Actually-measured physical properties
Modulus ofelasticity
E (kN/mm2)

Diameter
D(m)

Cedar

9.1

0.380

Pine

11.2

0.435

Length
L(m)

Mass
m(kg)

Densityρ(kg/m3)

2.0

156

687.8

1.0

72

634.9

2.0

179

602.3

Effective stiffness*3

k(kN/m)E D 2L
4*3: FEMA (2012)(2) Previous impact force calculation formulae
For a comparison with empirical results, the impact force calculation formulae were used aspresented by Matsutomi (1999), Ikeno and Tanaka (2003), Arikawa and Washizaki (2010), and
FEMA (2012), which are calculations that focus on wood as the impactor and addressedphenomena similar to the phenomena in this experiment. The coefficients in the calculation
formulae were set as indicated in Tables 8.3.2-3 and 8.3.2-4.
For the flow velocity in the calculation formula presented by FEMA (2012), the velocity(impact velocity) at the moment when wood strikes the abutment was used.

Appendix 8 - 59

Table 8.3.2-3 Setting of coefficients in the calculation formulae (Aerial experiments of logs)
Calculation formulae of impact
Setting
Coefficients
Remarksforce
value
Matsutomi (1999)
Ikeno and Tanaka (2003)

Arikawa and Washizaki (2010)
FEMA(2012)

CMA

1.0

S

5.0

CMA

1.0

γp

0.25

v

0.4

C

0

Aerial experiments

Aerial experiments

Aerial experiments

Table 8.3.2-4 Setting of coefficients in the calculation formulae (Underwater experiments of logs)
Calculation formulae of impact
Setting
Coefficients
Remarksforce
value
Matsutomi (1999)
Ikeno and Tanaka (2003)

Arikawa and Washizaki (2010)
FEMA(2012)

CMA

1.7

S

5.0

CMA

1.5

γp

0.25

v

0.4

C

0.3

Value of surge

Horizontal cylinder(3) Comparison of impact force estimation equations and empirical results
1) Aerial experiments using logs
Figure 8.3.2-4 is a comparison of empirical results with impact force calculation formulae
for a case where previous settings (catalog values) were used for the relationship of impact
force and impact velocity in aerial experiments using logs. The impact angle in the empiricalresults was 90° (vertical) for both. The distinctive features of each calculation formula are
given below.
• The estimation formulae presented by Arikawa and Washizaki (2010) and Matsutomi(1999) coincide well with the empirical results, and there is no significant difference in
the impact force between the case where previous settings were used and the case where
measured physical properties were used.
• The estimation formula presented by FEMA (2012) provided somewhat smaller resultsin comparison to the empirical results for a case where previous settings were used. On
the other hand, when measured physical properties were used, the impact force varied
significantly depending on the value of the effective axial rigidity.
• The estimation formula presented by Ikeno and Tanaka (2003) tended to have smaller

Appendix 8 - 60

results than the empirical results in all cases.
150

150

Cedar, 2m

100

150

Cedar, 1m

100

Experiment
Matsutomi(1999)
Ikeno et al.(2003)
Arikawa et al.(2010)
FEMA(2012)

F (kN)F (kN)F (kN)

100

50

50

50

0

0
0.0

1.0

2.0
V (m/s)3.0

Pine, 2m

0

0.0

4.0

1.0

2.0
V (m/s)

3.0

4.0

0.0

1.0

2.0
V (m/s)

3.0

4.0

2.0
V (m/s)3.0

4.0(1) Previous settings
Cedar, 2m

150

Cedar, 1m

150

F (kN)

100

Experiment
Matsutomi(1999)
Ikeno et al.(2003)
Arikawa et al.(2010)
FEMA(2012)

50

F (kN)

100

F (kN)

100

50

0

50

0
0.0

1.0

2.0
V (m/s)3.0

4.0

Pine, 2m

150

0
0.0

1.0

2.0
V (m/s)

3.0

4.0

0.0

1.0

(2) Actually-measured physical properties
Figure 8.3.2-3 Comparison between impact force calculation formulae and empirical results (Aerial
experiments of logs)
2) Underwater experiments using logs
Figure 8.3.2-3 is a comparison of empirical results with impact force calculation formulae
for a case where previous settings (catalog values) were used for the relationship of impact
force and impact velocity in underwater experiments using logs. The impact angle in theempirical results was 0° (horizontal) for all cases. The distinctive features of each calculation
formula are given below.
• The impact force found using the calculation formula presented by Ikeno and Tanaka(2003) coincided well with the empirical results.
• The impact force found using the calculation formulae presented by Matsutomi (1999),
Arikawa and Washizaki (2010) and FEMA (2012) was quite greater than that in theempirical results.
However, it needs to be kept in mind that, in contrast to the empirical results which show
a impact force using a impact angle of 0° (horizontal), the calculation formulae presented by
Matsutomi (1999) as well as Arikawa and Washizaki (2010) covered a impact angle of 90°(vertical), and a impact angle of 90° (vertical) was used for the effective axial rigidity aspresented by FEMA (2012).
Appendix 8 - 61

250

Experiment
Matsutomi(1999)
Ikeno et al.(2003)
Arikawa et al.(2010)
FEMA(2012)

F (kN)

150

200
150

F (kN)

200

Cedar, 2m

250

Cedar, 2m

100

100

50

50

0

0
0.0

1.0

2.0

3.0
V (m/s)

4.0

5.0

6.0

(1) Previous settings

0.0

1.0

2.0

3.0
V (m/s)

4.0

5.0

6.0

(2) Actually-measured physical properties

Figure 8.3.2-4 Comparison between impact force calculation formulae and empirical results(Underwater experiments of logs)
8.3.2.4. Impact force attributable to automobiles
The results of aerial experiments and underwater experiments were used to examine theapplicability of previous impact force calculation formulae.
(1) Previous impact force calculation formulae
Because there were no previous impact force calculation formulae that covered automobiles,
the applicability of FEMA (2012), which has a comparatively broad scope of applicability, wasexamined as a impact force calculation formula (see Appendix Section 8.3.1 for specifics
pertaining to the calculation formula).
For the effective axial rigidity k in the FEMA (2012) calculation formula, the two types ofsettings given in Table 8.3.2-5 were used. Also, the additional mass coefficient C for cases where
aerial experiments were conducted was 0.0. The additional mass coefficient C for cases where
underwater experiments were conducted took into account the estimated values according to
FEMA (2012) ranging from 0.0 to 0.3, and two settings were used, 0.0 and 0.3.
Table 8.3.2-5 Setting of coefficients in the calculation formulae (car)Calculation
Effective
formulae ofRemarks
stiffness
impact force
k(kN/m)
FEMA(2012)

1.5×106

Value of 20ft container by FEMA(2012)

1.35×102

Value of static load test(2) Comparison of impact force estimation equation and empirical results
Figure 8.3.2-5 is a comparison of the impact force calculation formula and empirical results
Appendix 8 - 62

for the relationship of impact force and impact velocity in underwater experiments using
automobiles.
1) Aerial experiments using automobiles
The features of the FEMA (2012) calculation formula are given below.
• For the impact force in a case where the value was used for axial rigidity of a 20 footcontainer according to FEMA (2012), calculation results that greatly exceeded theempirical results were obtained.
• For the impact force in a case where the value was used for axial rigidity which was
determined based upon static load tests, the calculation results somewhat exceeded theempirical results.
• Application of impact force calculation formulae to automobiles is difficult because there
are almost no previous references to effective axial rigidity or elasticity coefficient.
2) Underwater experiments using automobiles
The features of the FEMA (2012) calculation formula are given below.
• For the impact force in a case where the value was used for axial rigidity of a 20 feetcontainer according to FEMA (2012), calculation results that exceeded the empiricalresults were obtained.
• For the impact force in a case where the value was used for axial rigidity which was
determined based upon static load tests, the calculation results were below the empiricalresults.
• Application of impact force calculation formulae to automobiles is difficult because there
are almost no previous references to effective axial rigidity or elasticity coefficient.

100

20

Under water experiments

Aerial experiments
80

F (kN)F (kN)

15

10

5

60
40
20
0

0
0.0

0.5

V (m/s)1.0

1.5:FEMA (2012), k=1.5×106, C=0.0:FEMA (2012), k=1.35×102, C=0.0:Experiment

0.0

1.0

2.0
3.0
V (m/s)4.0

5.0:FEMA (2012), k=1.5×106, C=0.0:FEMA (2012), k=1.35×102, C=0.3:FEMA (2012), k=1.35×102, C=0.0:Experiment

Figure 8.3.2-5 Comparison between impact force calculation formulae and empirical results (car)Appendix 8 - 63

8.3.3. Previous analysis examples of methods for analyzing debris
Examples of previous analyses of methods for analyzing debris were consolidated. When theprevious analysis examples were broadly classified, they were separated into methods using the resultsof tsunami calculations in a plane two-dimensional model based upon the shallow water equation to
analyze the movement of debris, and methods expressing debris as a solid phase to simultaneously
calculate mutual interference with fluid (cross-sectional two-dimensional model or three-dimensionalmodel).
(1) Methods using the results of tsunami calculations based upon the shallow water equation to
analyze the movement of debris (plane two-dimensional model)• Goto (1983)• Fujii et al. (2005), and Fujii and Imamura (2010)• Kobayashi et al. (2005), Honda et al. (2009), Hashimoto et al. (2009), and Hashimoto etal. (2010)
Table 8.3.3-1 shows representative examples of previous analyses with the method using theresults of tsunami calculations based upon the shallow water equation to analyze the movementof debris.
(2) Methods expressing debris as a solid phase to simultaneously calculate mutual interference withfluid (cross-sectional two-dimensional or three-dimensional model)• Kawasaki et al. (2006)• Kawasaki and Hakamada (2007)• Yoneyama et al. (2008)• Yoneyama and Nagashima (2009)• Goto et al. (2009)• Ikeda and Arikawa (2014)
Table 8.3.3-2 shows representative examples of previous analyses with the method
expressing debris as a solid phase to simultaneously calculate mutual interference with fluid.
In addition to the calculation of tsunami debris, Fujii and Imamura (2010) put together
disaster scenarios and procedures for estimating damage due to tsunami debris.
Based upon the aforementioned examples of analyses of tsunami debris, it may be said thatplane two-dimensional analyses are practical for calculating the trajectory of debris across a widearea, and three-dimensional analyses and cross-sectional two-dimensional analyses are effectivemeans for ascertaining the behavior of debris when a tsunami strikes and the circumstances ofAppendix 8 - 64

impacts with structures.
Table 8.3.3-1 Representative examples of previous analysis with the method of solving the behavior
of debris using the result of the tsunami calculation based on shallow water equation
Author name

Fujii et al.

Objects

Ship(2005)

Honda et al.
(2009)

Ship

Analysismodel
Twodimensionalmodel

Twodimensional
model

Validity of theOverview of methods for analyzing debris

verification
method• Ship is modeled by distinct element method (DEM)and ship’s behavior is calculated by 6 degree of
freedom momentum equation on translation androtation.
• Morrison formula is applied to the fluid force
required for the calculation of the drift of the ship.
• Uses the water level and flow velocity of tsunami
analysis by shallow water equation.
• For the calculation of tsunami flow condition, use
storm surge and tsunami simulator (STOC).
• The momentum equation concerning the drifting of
the ship is formulated assuming that the main
movement is front and near, right and left, and yaw
direction, and a hull moving coordinate system whose
origin is the hull center of gravity is used.
• The fluid force required to calculate the drift of a ship
is based on the extension of Morrison equation.
• Consider impact of debris with the ground andbuildings and mutual impact of debris.

Appendix 8 - 65

Comparison of
the hydraulicmodel
experiment

Test calculation
and applied tothe actual terrain

Table 8.3.3-2 Representative examples of previous analysis with the method of expressing debris insolid phase to calculation mutual interference with fluid simultaneously
Author name

Yoneyama
andNagashima

Objects

Wood

Container(2009)

Overview of methods for analyzing debris

model
Threedimensionalmodel(2009)

Goto et al.

Validity of theAnalysisThreedimensionalmodel

verification
method• Three-dimensional Numerical Analysis Method
considering translational 3 DOF (degree of
freedom) and 3 DOF rotation.
• The fundamental equation of the fluid is the sameas Yoneyama et al. (2008).
• Set the inertia main axis coordinate system withthe center of gravity of the rigid body as the origin
and Formulation of the momentum equation of thedebris center of gravity and the momentum
equation of the rotary motion about the center ofgravity of the debris.
• The fluid force experienced by the debris also
takes into consideration the pressure and adhesive
force and the impact of the debris against the wall
surface.
• Fluid analysis uses the MPS method, and themomentum equation uses the Navier-Stokes
equation.
• The container constitutes a plurality of solid phaseparticles by a rigid body connected model.
• The fluid acting on the container is calculated byincorporating the rigid constituent particles
together with the fluid particles into theintergranular interaction model.

Comparison of
the hydraulicmodel
experiment by
Ikeno et al.
(2003)

Comparison of
the hydraulicmodel
experiment by
Arikawa et al.
(2007)[Appendix 8 References]
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